{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\sqrt{2} x-3y=1 \\\\ & 2x+\\sqrt{2} y=-2 \\\\ \\end{align} \\right.$ l\u00e0 ","select":["A. $\\left(\\dfrac{6-\\sqrt{2}}{8};\\dfrac{\\sqrt{2}+1}{4}\\right)$ ","B. $\\left(\\dfrac{-6-\\sqrt{2}}{8};\\dfrac{\\sqrt{2}-1}{4}\\right)$","C. $\\left(\\dfrac{-6+\\sqrt{2}}{8};\\dfrac{-\\sqrt{2}-1}{4}\\right)$","D. $\\left(\\dfrac{6+\\sqrt{2}}{8};\\dfrac{-\\sqrt{2}+1}{4}\\right)$"],"hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1: Nh\u00e2n hai v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t v\u1edbi $\\sqrt{2}$","explain":"<span class='basic_left'> Nh\u00e2n hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t v\u1edbi $\\sqrt{2}$ ta \u0111\u01b0\u1ee3c: $\\left\\{ \\begin{align} & 2x-3\\sqrt{2}y=\\sqrt{2} \\\\ & 2x+\\sqrt{2} y=-2 \\\\ \\end{align} \\right.$<br\/>Tr\u1eeb t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai cho t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t c\u1ee7a h\u1ec7, ta \u0111\u01b0\u1ee3c:<br\/> $4\\sqrt{2}y=-2-\\sqrt{2} \\Leftrightarrow y=\\dfrac{-2-\\sqrt{2}}{4\\sqrt{2}}$$\\Leftrightarrow y=\\dfrac{\\left( -2-\\sqrt{2} \\right)\\sqrt{2}}{4.2}\\Leftrightarrow y=\\dfrac{-\\sqrt{2}-1}{4}$<br\/>Thay $y=\\dfrac{-\\sqrt{2}-1}{4}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, ta \u0111\u01b0\u1ee3c:<br\/>$\\begin{aligned} & 2x+\\sqrt{2}.\\dfrac{-\\sqrt{2}-1}{4}=-2 \\\\ & \\Leftrightarrow 2x=-2+\\dfrac{2+1\\sqrt{2}}{4} \\\\ & \\Leftrightarrow 2x=\\dfrac{-6+\\sqrt{2}}{4} \\\\ & \\Leftrightarrow x=\\dfrac{-6+\\sqrt{2}}{8} \\\\ \\end{aligned}$ <br\/> Suy ra $(\\dfrac{-6+\\sqrt{2}}{8};\\dfrac{-\\sqrt{2}-1}{4})$ l\u00e0 nghi\u1ec7m duy nh\u1ea5t c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span> <br\/> <span class='basic_green'> Ch\u00fa \u00fd:<\/span> <br\/> $\\bullet $ Mu\u1ed1n kh\u1eed \u1ea9n n\u00e0o th\u00ec \u0111\u01b0a \u1ea9n \u0111\u00f3 trong hai ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 c\u00f9ng h\u1ec7 s\u1ed1 ho\u1eb7c c\u00f3 h\u1ec7 s\u1ed1 \u0111\u1ed1i nhau.<br\/> $\\bullet $ \u1ea8n mu\u1ed1n kh\u1eed c\u00f3 h\u1ec7 s\u1ed1 \u0111\u1ed1i nhau ($+$ v\u00e0 $-$) th\u00ec ta c\u1ed9ng t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 v\u1edbi nhau <br\/> $\\bullet $ \u1ea8n mu\u1ed1n kh\u1eed c\u00f3 h\u1ec7 s\u1ed1 c\u00f9ng d\u1ea5u ($+$ v\u00e0 $+$ ho\u1eb7c $-$ v\u00e0 $-$) th\u00ec ta tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau.<\/span><\/span> ","column":2}]}],"id_ques":271},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"],["-2"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align} & 10x-9y=8 \\\\ & 15x+21y=-57 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (_input_;_input_) ","explain":"<span class='basic_left'><br\/> <span class='basic_green'> H\u01b0\u1edbng d\u1eabn <\/span> <br\/> Nh\u00e2n hai v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai v\u1edbi $\\dfrac{2}{3}$ r\u1ed3i d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1 \u0111\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> <span class='basic_green'> B\u00e0i gi\u1ea3i <\/span><br\/> Nh\u00e2n hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai v\u1edbi $\\dfrac{2}{3}$ r\u1ed3i l\u1ea5y t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 tr\u1eeb \u0111i t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & 10x-9y=8 \\\\ & 15x+21y=-57 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 10x-9y=8 \\\\ & 10x+14y=-38 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 23y=-46 \\\\ & 10x-9y=8 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=-2 \\\\ & 10x=-10 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=-1 \\\\ & y=-2 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(-1;-2)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $-1$ v\u00e0 $-2.$ <\/span> "}]}],"id_ques":272},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"],["-2"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align} & 3,3x+4,2y=1,5 \\\\ & 9x+14y=-1 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (_input_;_input_) ","explain":"<span class='basic_left'> Chia hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t cho $0,3$ r\u1ed3i l\u1ea5y t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t tr\u1eeb \u0111i t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & 3,3x+4,2y=1,5 \\\\ & 9x+14y=-1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 11x+14y=5 \\\\ & 9x+14y=-1 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 2x=6 \\\\ & 9x+14y=-1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=3 \\\\ & 9.3+14y=-1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=3 \\\\ & y=-2 \\\\ \\end{align} \\right.$<br\/> Suy ra $(3;-2)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $3$ v\u00e0 $-2.$ <\/span><\/span>"}]}],"id_ques":273},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" X\u00e1c \u0111\u1ecbnh $a$ \u0111\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <br\/> $\\left\\{ \\begin{align} & x-y=1 \\\\ & 2x+y=2 \\\\ \\end{align} \\right.$ (I) $\\,\\,\\,\\,\\,\\,\\,\\,$ $\\left\\{ \\begin{align} & ax-2y=2 \\\\ & x+ay=1 \\\\ \\end{align} \\right.$ (II) <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $a=$ _input_","hint":"Hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng n\u1ebfu ch\u00fang c\u00f3 chung t\u1eadp nghi\u1ec7m. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/>B\u01b0\u1edbc 1: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I)<br\/>B\u01b0\u1edbc 2: H\u1ec7 (I) v\u00e0 (II) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng n\u1ebfu nghi\u1ec7m c\u1ee7a h\u1ec7 (I) l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 (II). Ta thay nghi\u1ec7m h\u1ec7 (I) v\u00e0o h\u1ec7 (II) \u0111\u1ec3 t\u00ecm $a$<br\/>B\u01b0\u1edbc 3: Th\u1eed l\u1ea1i v\u1edbi $a$ v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c, h\u1ec7 (I) v\u00e0 h\u1ec7 (II) c\u00f3 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/> Ta c\u00f3: $\\left\\{ \\begin{align} & x-y=1 \\\\ & 2x+y=2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=y+1 \\\\ & 2(y+1)+y=2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=y+1 \\\\ & 3y=0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & y=0 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(1;0)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) <br\/> \u0110\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng n\u1ebfu $(1;0)$ l\u00e0 nghi\u1ec7m c\u1ee7a (II) <br\/> T\u1ee9c l\u00e0 $\\left\\{ \\begin{align} & a.1-2.0=2 \\\\ & 1+a.0=1 \\\\ \\end{align} \\right.$$\\Rightarrow a=2$ <br\/> Ng\u01b0\u1ee3c l\u1ea1i, v\u1edbi $a=2$ h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (II) tr\u1edf th\u00e0nh <br\/> $\\left\\{ \\begin{align} & 2x-2y=2 \\\\ & x+2y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 3x=3 \\\\ & y=0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & x+2y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & 1+2y=1 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & y=0 \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( 1;0 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (II) <br\/> V\u1eady v\u1edbi $a=2$ \u0111\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $2.$ <\/span>"}]}],"id_ques":274},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-13"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 3x+2y=-2 \\\\ & x+2y=6 \\\\ \\end{align} \\right.$ (I) <br\/> <\/b> T\u00ecm $m$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=1 \\\\ & 2x-y=m \\\\ \\end{align} \\right.$ (II) ? <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $m=$ _input_","hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) r\u1ed3i th\u1ebf nghi\u1ec7m v\u00e0o h\u1ec7 (II). <br\/>Ch\u00fa \u00fd: Hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng n\u1ebfu ch\u00fang c\u00f3 c\u00f9ng t\u1eadp nghi\u1ec7m.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> (I) $\\Leftrightarrow \\left\\{ \\begin{align} & x=6-2y \\\\ & 3\\left( 6-2y \\right)+2y=-2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=6-2y \\\\ & 18-6y+2y=-2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& x=6-2y \\\\ & 4y=20 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=6-2.5 \\\\ & y=5 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=-4 \\\\ & y=5 \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( -4;5 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) <br\/> \u0110\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi h\u1ec7 (II) th\u00ec $(-4;5)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 (II) <br\/> $\\Leftrightarrow\\left\\{ \\begin{align} & -4+5=1 \\,\\text {(\u0111\u00fang)}\\\\ & 2.(-4)-5=m \\\\ \\end{align} \\right.$ <br\/> $\\Leftrightarrow -8-5=m$$\\Leftrightarrow m=-13$ <br\/> Ng\u01b0\u1ee3c l\u1ea1i, v\u1edbi $m=-13$ h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (II) tr\u1edf th\u00e0nh <br\/> $\\left\\{ \\begin{align} & x+y=1\\,(1) \\\\ & 2x-y=-13\\,(2) \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=1-y \\\\ & 2\\left( 1-y \\right)-y=-13 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=1-y \\\\ & -3y=-15 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=1-y \\\\ & y=5 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=-4 \\\\ & y=5 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(-4;5)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (II) <br\/> V\u1eady v\u1edbi $m=-13$ th\u00ec hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $-13.$ <\/span>"}]}],"id_ques":275},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Cho c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau: <br\/> $\\left\\{ \\begin{align} & 4x+3y=7 \\\\ & 2x+5y=-7 \\\\ \\end{align} \\right.$ (I); $\\left\\{ \\begin{align} & 4x-3y=21 \\\\ & 2x-5y=21 \\\\ \\end{align} \\right.$ (II) v\u00e0 $\\left\\{ \\begin{align} & -5x-3y=-11 \\\\ & 2x+9y=-19 \\\\ \\end{align} \\right.$ (III) <br\/> Hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau? ","select":["A. H\u1ec7 (I) v\u00e0 (II) ","B. H\u1ec7 (II) v\u00e0 (III)","C. H\u1ec7 (I) v\u00e0 (III)"],"explain":"<span class='basic_left'>Nh\u00e2n hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 (I) v\u1edbi $2$ r\u1ed3i tr\u1eeb t\u1eebng v\u1ebf cho t\u1eebng v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & 4x+3y=7 \\\\ & 2x+5y=-7 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 4x+3y=7 \\\\ & 4x+10y=-14 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 7y=-21 \\\\ & 2x+5y=-7 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=-3 \\\\ & 2x+5.(-3)=-7 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=-3 \\\\ & 2x=8 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=4 \\\\ & y=-3 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(4;-3)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) <br\/>Nh\u00e2n hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 (II) v\u1edbi $2$ r\u1ed3i tr\u1eeb t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t cho t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & 4x-3y=21 \\\\ & 2x-5y=21 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 4x-3y=21 \\\\ & 4x-10y=42 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 7y=-21 \\\\ & 2x-5y=21 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=-3 \\\\ & 2x-5.(-3)=21 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=3 \\\\ & y=-3 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(3;-3)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> Nh\u00e2n hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t c\u1ee7a h\u1ec7 (III) v\u1edbi $2$ v\u00e0 nh\u00e2n hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai v\u1edbi $5$ r\u1ed3i c\u1ed9ng hai v\u1ebf c\u1ee7a hai ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c:<br\/> $\\left\\{ \\begin{align} & -5x-3y=-11 \\\\ & 2x+9y=-19 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & -10x-6y=-22 \\\\ & 10x+45y=-95 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 39y=-117 \\\\ & 2x+9y=31 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=-3 \\\\ & 2x+9.(-3)=-19 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=4\\\\ & y=-3 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(4;-3)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (III) <br\/> Suy ra h\u1ec7 (I) v\u00e0 (III) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C .<\/span>","column":3}]}],"id_ques":276},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"C\u1eb7p s\u1ed1 $(-13; -5)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o sau \u0111\u00e2y?","select":["A. $\\left\\{ \\begin{align}& x-y=3 \\\\ & x+y=5 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align}& -4x-y=-19 \\\\ & -5x+3y=-62 \\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align}& x-3y=2 \\\\ & -2x+5y=1 \\\\ \\end{align} \\right.$"],"hint":"Gi\u1ea3i t\u1eebng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\bullet\\left\\{ \\begin{align}& x-y=3 \\\\ & x+y=5 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& x=y+3\\,(1) \\\\ & x+y=5\\,(2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $x=y+3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $y+3+y=5$$\\Leftrightarrow 2y=2$$\\Leftrightarrow y=1$ <br\/> Th\u1ebf $y=1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1) <br\/> $\\Rightarrow x=1+3=4$ <br\/> Suy ra $\\left( 4;1 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\bullet\\left\\{ \\begin{align}& -4x-y=-19 \\\\ & -5x+3y=-62 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& y=19-4x\\,(3) \\\\ & -5x+3y=-62\\,(4) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y=19-4x$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (4), ta \u0111\u01b0\u1ee3c: <br\/> $-5x+3(19-4x)=-62$$\\Leftrightarrow -5x+57-12x=-62$$\\Leftrightarrow -17x=-119$$\\Leftrightarrow x=7$ <br\/> Th\u1ebf $x=7$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (3) <br\/> $\\Rightarrow y=19-4.7=-9$ <br\/> Suy ra $\\left( 7;-9 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\bullet\\left\\{ \\begin{align}& x-3y=2 \\\\ & -2x+5y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& x=3y+2\\,(5) \\\\ & -2x+5y=1\\,(6) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $x=3y+2$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (6), ta \u0111\u01b0\u1ee3c: <br\/> $ -2(3y+2)+5y=1$$\\Leftrightarrow -6y-4+5y=1$$\\Leftrightarrow -y-4=1$$\\Leftrightarrow y=-5$ <br\/> Th\u1ebf $y=-5$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (5) <br\/> $\\Rightarrow x=3.(-5)+2=-13$ <br\/> Suy ra $(-13;-5)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span>","column":3}]}],"id_ques":277},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 2x+y=-1 \\\\ & 2x+5y=3 \\\\ \\end{align} \\right.$ (I) <br\/> T\u00ecm $m$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x+3y=2 \\\\ & 3mx+\\left( {{m}^{2}}+8 \\right)y=4m+2 \\\\ \\end{align} \\right.$ (II) ?","select":["A. $\\left[ \\begin{align} & m=1 \\\\ & m=6 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & m=-1 \\\\ & m=-6 \\\\ \\end{align} \\right.$","C. $m=1$ ","D. $m=6$ "],"explain":"<span class='basic_left'> L\u1ea5y t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 (I) tr\u1eeb \u0111i t\u1eebng v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & 2x+y=-1 \\\\ & 2x+5y=3 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 4y=4 \\\\ & 2x+y=-1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=1 \\\\ & 2x+1=-1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=-1 \\\\ & y=1 \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( -1;1 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> \u0110\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi (II) th\u00ec $(-1;1)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (II) <br\/> $\\left\\{ \\begin{align} & -1+3.1=2\\, \\text{(\u0111\u00fang)} \\\\ & -3m+\\left( {{m}^{2}}+8 \\right).1=4m+2 \\\\ \\end{align} \\right.$ <br\/> $\\Leftrightarrow {{m}^{2}}-7m+6=0$ $\\Leftrightarrow \\left[ \\begin{align} & m=1 \\\\ & m=6 \\\\ \\end{align} \\right.$ <br\/> Ng\u01b0\u1ee3c l\u1ea1i v\u1edbi $m=1$, h\u1ec7 th\u1ee9 hai tr\u1edf th\u00e0nh <br\/> $\\left\\{ \\begin{align}& x+3y=2 \\\\ & 3x+9y=6 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x+3y=2 \\\\ & x+3y=2 \\\\ \\end{align} \\right.$ <br\/> H\u1ec7 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m (lo\u1ea1i) <br\/> V\u1edbi $m=6$ h\u1ec7 th\u1ee9 hai tr\u1edf th\u00e0nh <br\/> $\\left\\{ \\begin{align} & x+3y=2 \\\\ & 18x+44y=13 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=2-3y \\\\ & 9x+22y=13 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=2-3y \\\\ & 9\\left( 2-3y \\right)+22y=13 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=2-3y \\\\ & -5y=-5 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=1 \\\\ & x=-1 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(-1;1)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (II) <br\/> V\u1eady v\u1edbi $m=6$ th\u00ec hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span>","column":2}]}],"id_ques":278},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"],["5"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $a$ v\u00e0 $b$ sao cho $5a-4b=-5$ v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng $ax + by = -1$ \u0111i qua \u0111i\u1ec3m $A(-7; 4)$ <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(a; b)=$(_input_;_input_)","explain":"<span class='basic_left'> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: $5a-4b=-5$ (1) <br\/> Do \u0111\u01b0\u1eddng th\u1eb3ng $ax + by = -1$ \u0111i qua \u0111i\u1ec3m $A$ n\u00ean t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $A$ th\u1ecfa m\u00e3n \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 <br\/> $\\Rightarrow -7a + 4b = -1$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow a, b$ th\u1ecfa m\u00e3n h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $\\left\\{ \\begin{align} & 5a-4b=-5 \\\\ & -7a+4b=-1 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & -2a=-6 \\\\ & -7a+4b=-1 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & a=3 \\\\ & -7.3+4b=-1 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & a=3 \\\\ & 4b=20 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & a=3 \\\\ & b=5 \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $3$ v\u00e0 $5.$ <\/span>"}]}],"id_ques":279},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a $a$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau c\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t $\\left\\{ \\begin{align} & x-y=5 \\\\ & 2x+ay=a \\\\ \\end{align} \\right.$","select":["A. $a= 2$ ","B. $a\\ne 2$","C. $a= -2$","D. $a\\ne -2$ "],"explain":"<span class='basic_left'><br\/> <span class='basic_green'> H\u01b0\u1edbng d\u1eabn <\/span> <br\/> Ta bi\u1ebfn \u0111\u1ed5i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng quy t\u1eafc th\u1ebf ho\u1eb7c c\u1ed9ng \u0111\u1ea1i s\u1ed1. Khi \u0111\u00f3 ta thu \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh m\u00e0 trong \u0111\u00f3 c\u00f3 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n d\u1ea1ng $ax=b$ (*)<br\/>Khi \u0111\u00f3 s\u1ed1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh s\u1ebd b\u1eb1ng s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (*)<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 nghi\u1ec7m duy nh\u1ea5t $\\Leftrightarrow a \\ne 0$<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m $\\Leftrightarrow a=b=0$<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) v\u00f4 nghi\u1ec7m n\u1ebfu $a=0$ v\u00e0 $b \\ne 0$<br\/> <span class='basic_green'> B\u00e0i gi\u1ea3i <\/span> <br\/>Ta c\u00f3: <br\/>$\\left\\{ \\begin{aligned} & x-y=5 \\\\ & 2x+ay=a \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=y+5 \\\\ & 2\\left( y+5 \\right)+ay=a \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=y+5 \\\\ & \\left( 2+a \\right)y=a-10\\,\\,\\,\\,\\left( 1 \\right) \\\\ \\end{aligned} \\right.$ <br\/>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 nghi\u1ec7m duy nh\u1ea5t $\\Leftrightarrow 2+a\\ne 0\\Leftrightarrow a\\ne -2$ <br\/> V\u1eady $a\\ne -2$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 duy nh\u1ea5t nghi\u1ec7m <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span> C\u00e1ch gi\u1ea3i kh\u00e1c: H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t n\u1ebfu \u0111\u1ed3 th\u1ecb c\u1ee7a c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh trong h\u1ec7 l\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c kh\u00e1c nhau.<br\/>X\u00e9t hai tr\u01b0\u1eddng h\u1ee3p: $a=0$ v\u00e0 $a\\ne 0$<br\/>Tr\u01b0\u1eddng h\u1ee3p 1: $a = 0$, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & x-y=5 \\\\ & 2x=0 \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align} & x = 0 \\\\ & -y = 5 \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align} & x=0 \\\\ & y=-5 \\\\ \\end{align} \\right.$ <br\/> V\u1eady $a = 0$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $a\\ne 0$ <br\/> $\\left\\{ \\begin{align} & x-y=5 \\\\ & 2x+ay=a \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align} & y = x - 5 \\, (2) \\\\ & y=\\dfrac{-2}{a}x + 1 \\, (3) \\\\ \\end{align} \\right.$ <br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng (2) v\u00e0 (3) c\u1eaft nhau <br\/> $\\Rightarrow \\dfrac{-2}{a} \\ne 1 \\Leftrightarrow a \\ne -2$ <br\/> V\u1eady $a\\ne -2$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 duy nh\u1ea5t nghi\u1ec7m <br\/><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span> V\u1edbi nh\u1eefng b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a tham s\u1ed1 $m$ th\u00ec ta n\u00ean d\u00f9ng c\u00e1ch 1 cho \u0111\u01a1n gi\u1ea3n v\u00e0 ng\u1eafn g\u1ecdn. V\u1edbi nh\u1eefng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 s\u1ed1 c\u1ee5 th\u1ec3 th\u00ec ta c\u00f3 th\u1ec3 d\u00f9ng c\u00e1ch 2.","column":4}]}],"id_ques":280},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a $m$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau v\u00f4 nghi\u1ec7m $\\left\\{ \\begin{align} & mx+y=3 \\\\ & x+my=2 \\\\ \\end{align} \\right.$","select":["A. $m=\\pm 1$ ","B. $m\\ne \\pm 1$","C. $m\\ne \\dfrac{3}{2}$","D. $m= \\dfrac{3}{2}$ "],"explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\begin{aligned} & \\,\\,\\,\\,\\,\\,\\,\\left\\{ \\begin{aligned} & mx+y=3 \\\\ & x+my=2 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=-mx+3 \\\\ & x+m\\left( -mx+3 \\right)=2 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=-mx+3 \\\\ & x-{{m}^{2}}x+3m=2 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=-mx+3 \\\\ & \\left( 1-{{m}^{2}} \\right)x=2-3m\\,\\,\\,\\left( * \\right) \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ <br\/>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m<br\/> $\\Leftrightarrow $ Ph\u01b0\u01a1ng tr\u00ecnh (*) v\u00f4 nghi\u1ec7m $\\Leftrightarrow \\left\\{ \\begin{aligned} & 1-{{m}^{2}}=0 \\\\ & 2-3m\\ne 0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & m=\\pm 1 \\\\ & m\\ne \\dfrac{2}{3} \\\\ \\end{aligned} \\right.\\Leftrightarrow m=\\pm 1$ <br\/> Suy ra $m=\\pm 1$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span>","column":2}]}],"id_ques":281},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"],["-3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 3x-y=-m \\\\ & 3x-{{m}^{2}}y=-3 \\\\ \\end{align} \\right.$ <\/b> <br\/> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi $m=0?$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y)=$ (_input_;_input_)","explain":"<span class='basic_left'> V\u1edbi $m=0$, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh <br\/> $\\left\\{ \\begin{align} & 3x-y=0 \\\\ & 3x=-3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=-1 \\\\ & 3.(-1)-y=0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=-1 \\\\ & y=-3 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(-1;-3)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $-1$ v\u00e0 $-3.$<\/span>"}]}],"id_ques":282},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"select":["A. ($\\dfrac{1}{3};\\dfrac{1}{3}$)","B. ($\\dfrac{1}{3};\\dfrac{2}{3}$)","C. ($\\dfrac{1}{3};\\dfrac{1}{2}$)"],"ques":" Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & mx+y=1 \\\\ & 4x+my=2 \\\\ \\end{align} \\right.$ <br\/> <br\/> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh khi $m = 1$ <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y)=$ (?; ?)","explain":"<span class='basic_left'> V\u1edbi $m=1$ h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh: $\\left\\{ \\begin{align} & x+y=1\\,(1) \\\\ & 4x+y=2\\,(2) \\\\ \\end{align} \\right.$ <br\/> L\u1ea5y t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u1eeb \u0111i t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & x+y=1\\,(1) \\\\ & 4x+y=2\\,(2) \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 3x=1 \\\\ & x+y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\dfrac{1}{3} \\\\ & y=\\dfrac{2}{3} \\\\ \\end{align} \\right.$ <br\/> "}]}],"id_ques":283},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & mx+y=1 \\\\ & 4x+my=2 \\\\ \\end{align} \\right.$ <br\/> T\u00ecm $m$ \u0111\u1ec3 h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n $x-y=1$ <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $m=$ _input_","explain":"<span class='basic_left'> Nh\u00e2n t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi $m$ r\u1ed3i tr\u1eeb t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai cho t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & mx+y=1 \\\\ & 4x+my=2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 4mx+4y=4 \\\\ & 4mx+{{m}^{2}}y=2m \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & \\left( {{m}^{2}}-4 \\right)y=2m-4\\,(*) \\\\ & mx+y=1 \\\\ \\end{align} \\right.$ <br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 nghi\u1ec7m duy nh\u1ea5t<br\/> $\\Leftrightarrow {{m}^{2}}-4\\ne 0$$\\Leftrightarrow m\\ne \\pm 2$ <br\/> Khi \u0111\u00f3 $\\left\\{ \\begin{align} & y=\\dfrac{2\\left( m-2 \\right)}{{{m}^{2}}-4}=\\dfrac{2}{m+2} \\\\ & mx+\\dfrac{2}{m+2}=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=\\dfrac{2}{m+2} \\\\ & x=\\dfrac{1}{m+2} \\\\ \\end{align} \\right.$ <br\/> M\u00e0 $x-y=1$$\\Leftrightarrow \\dfrac{1}{m+2}-\\dfrac{2}{m+2}=1$$\\Leftrightarrow \\dfrac{-1}{m+2}=1\\Leftrightarrow m+2=-1$$\\Leftrightarrow m=-3$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $m=-3.$<\/span>"}]}],"id_ques":284},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $2x+3y=20;\\,3x-5y=11$ v\u00e0 $x+y=9$ c\u00f3 \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m kh\u00f4ng?","select":["A. C\u00f3 ","B. Kh\u00f4ng"],"hint":"Ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy n\u1ebfu ch\u00fang c\u00f9ng \u0111i qua m\u1ed9t \u0111i\u1ec3m","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: T\u00ecm giao \u0111i\u1ec3m $A$ c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng $2x+3y=20;\\,3x-5y=11$ <br\/>B\u01b0\u1edbc 2: Ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy n\u1ebfu \u0111\u01b0\u1eddng th\u1eb3ng $x+y=9$ \u0111i qua $A$. Thay t\u1ecda \u0111\u1ed9 A v\u00e0o $x+y=9$ v\u00e0 ki\u1ec3m tra<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/>$\\begin{aligned} & \\,\\,\\,\\,\\,\\,\\left\\{ \\begin{aligned} & 2x+3y=20 \\\\ & 3x-5y=11 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 6x+9y=60 \\\\ & 6x-10y=22 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 19y=38 \\\\ & 6x-10y=22 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=2 \\\\ & 6x=22+10y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=2 \\\\ & 6x=22+10.2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=2 \\\\ & 6x=42 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=2 \\\\ & x=7 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ <br\/>Suy ra hai \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi hai ph\u01b0\u01a1ng tr\u00ecnh $2x+3y=20$ v\u00e0 $3x-5y=11$ c\u1eaft nhau t\u1ea1i $A(7;2)$<br\/>Thay t\u1ecda \u0111\u1ed9 c\u1ee7a A v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh: $x+y=9,$ ta c\u00f3: $7+2=9$ (th\u1ecfa m\u00e3n)<br\/>Suy ra \u0111\u01b0\u1eddng th\u1eb3ng $x+y=9$ c\u0169ng \u0111i qua $A$ hay ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00e3 cho \u0111\u1ed3ng quy<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 A <\/span><br\/><b>C\u00e1ch kh\u00e1c:<\/b> V\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a 3 \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi 3 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 ki\u1ec3m tra","column":2}]}],"id_ques":285},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $m$ \u0111\u1ec3 ba \u0111\u01b0\u1eddng th\u1eb3ng sau \u0111\u1ed3ng quy: <br\/> $\\left( {{d}_{1}} \\right): 5x+11y=8,\\left( {{d}_{2}} \\right):10x-7y=74,\\left( {{d}_{3}} \\right):4mx+\\left( 2m-1 \\right)y=m+2.$<\/span>","select":["A. $m=-2$ ","B. $m=1$","C. $m=0$","D. $m=3$"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: T\u00ecm giao \u0111i\u1ec3m $A$ c\u1ee7a $(d_1)$ v\u00e0 $(d_2)$<br\/>B\u01b0\u1edbc 2: Ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy n\u1ebfu $(d_3)$ \u0111i qua $A$. Thay t\u1ecda \u0111\u1ed9 A v\u00e0o $(d_3)$ \u0111\u1ec3 t\u00ecm $m$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Giao \u0111i\u1ec3m $A$ c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng $(d_1)$ v\u00e0 $(d_2)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $\\left\\{ \\begin{align} & 5x+11y=8 \\\\ & 10x-7y=74 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 10x+22y=16 \\\\ & 10x-7y=74 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 29y=-58 \\\\ & 5x+11y=8 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & y=-2 \\\\ & 5x+11.(-2)=8 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & y=-2 \\\\ & 5x=30 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=6 \\\\ & y=-2 \\\\ \\end{align} \\right.$ <br\/> Suy ra $A (6; -2)$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng $(d_1)$ v\u00e0 $(d_2)$ <br\/> \u0110\u1ec3 ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy khi v\u00e0 ch\u1ec9 khi $A \\in d_3$ <br\/> $\\Rightarrow$ T\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $A$ th\u1ecfa m\u00e3n \u0111\u01b0\u1eddng th\u1eb3ng $(d_3)$ <br\/> $\\Rightarrow 4m.6 + (2m-1).(-2) = m + 2$ $\\Leftrightarrow 24m - 4m + 2 = m + 2 \\Leftrightarrow 19m = 0$ $ \\Leftrightarrow m = 0$ <br\/> V\u1eady v\u1edbi $m=0$ th\u00ec ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span>","column":4}]}],"id_ques":286},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"C\u1eb7p s\u1ed1 $(\\sqrt{3}; -\\sqrt{2})$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o sau \u0111\u00e2y?","select":["A. $\\left\\{ \\begin{align} & \\sqrt{3}x-2\\sqrt{2}y=7 \\\\ & \\sqrt{2}x+3\\sqrt{3}y=-2\\sqrt{6} \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & \\sqrt{2}x+\\sqrt{3}y=5 \\\\ & \\sqrt{3}x-\\sqrt{2}y=0 \\\\ \\end{align} \\right.$"],"explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\bullet\\left\\{ \\begin{align} & \\sqrt{3}x-2\\sqrt{2}y=7 \\\\ & \\sqrt{2}x+3\\sqrt{3}y=-2\\sqrt{6} \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & \\sqrt{6}x-4y=7\\sqrt{2} \\\\ & \\sqrt{6}x+9y=-6\\sqrt{2} \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 13y=-13\\sqrt{2} \\\\ & \\sqrt{3}x-2\\sqrt{2}y=7 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & y=-\\sqrt{2} \\\\ & \\sqrt{3}x+4=7 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=-\\sqrt{2} \\\\ & \\sqrt{3}x=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\sqrt{3} \\\\ & y=-\\sqrt{2} \\\\ \\end{align} \\right.$ <br\/> Suy ra $(\\sqrt{3}; -\\sqrt{2})$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\bullet\\left\\{ \\begin{align} & \\sqrt{2}x+\\sqrt{3}y=5 \\\\ & \\sqrt{3}x-\\sqrt{2}y=0 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 2x+\\sqrt{6}y=5\\sqrt{2} \\\\ & 3x-\\sqrt{6}y=0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 5x=5\\sqrt{2} \\\\ & \\sqrt{3}x-\\sqrt{2}y=0 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\sqrt{2} \\\\ & \\sqrt{3}.\\sqrt{2}-\\sqrt{2}y=0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\sqrt{2} \\\\ & y=\\sqrt{3} \\\\ \\end{align} \\right.$<br\/> Suy ra $(\\sqrt{2}; \\sqrt{3})$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> V\u1eady $(\\sqrt{3}; -\\sqrt{2})$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\sqrt{3}x-2\\sqrt{2}y=7 \\\\ & \\sqrt{2}x+3\\sqrt{3}y=-2\\sqrt{6} \\\\ \\end{align} \\right.$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span>","column":2}]}],"id_ques":287},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["5"],["3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<b> C\u00e2u 1:<\/b> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & X+Y=8 \\\\ & 2X-3Y=1 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(X;Y)=$ (_input_; _input_)","explain":"<span class='basic_left'> Nh\u00e2n ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t v\u1edbi $3$ r\u1ed3i c\u1ed9ng t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7, ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align} & X+Y=8 \\\\ & 2X-3Y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 3X+3Y=24\\,(1) \\\\ & 2X-3Y=1\\,(2) \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 5X=25 \\\\ & X+Y=8 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & X=5 \\\\ & 5+Y=8 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & X=5 \\\\ & Y=3 \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( 5;3 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $5$ v\u00e0 $3.$<\/span>"}]}],"id_ques":288},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. ($-\\dfrac{4}{5};\\dfrac{7}{3}$)","B. ($\\dfrac{4}{5};\\dfrac{2}{3}$)","C. ($\\dfrac{1}{3};\\dfrac{7}{3}$)"],"ques":"<b> C\u00e2u 2: <\/b> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\dfrac{1}{x+1}+\\dfrac{1}{y-2}=8 \\\\ & \\dfrac{2}{x+1}-\\dfrac{3}{y-2}=1 \\\\ \\end{align} \\right.$ <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y)=$ (?;?)","explain":"<span class='basic_left'> \u0110i\u1ec1u ki\u1ec7n: $\\left\\{ \\begin{align} & x+1\\ne 0 \\\\ & y-2\\ne 0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x\\ne -1 \\\\ & y\\ne 2 \\\\ \\end{align} \\right.$ <br\/> \u0110\u1eb7t $\\left\\{ \\begin{align} & \\dfrac{1}{x+1}=X \\\\ & \\dfrac{1}{y-2}=Y \\\\ \\end{align} \\right.$ <br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh: $\\left\\{ \\begin{align} & X+Y=8 \\\\ & 2X-3Y=1 \\\\ \\end{align} \\right.$ <br\/> Theo c\u00e2u 1, ta c\u00f3: $\\left\\{ \\begin{align} & X=5 \\\\ & Y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & \\dfrac{1}{x+1}=5 \\\\ & \\dfrac{1}{y-2}=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x+1=\\dfrac{1}{5} \\\\ & y-2=\\dfrac{1}{3} \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\dfrac{-4}{5} \\\\ & y=\\dfrac{7}{3} \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( \\dfrac{-4}{5};\\dfrac{7}{3} \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> "}]}],"id_ques":289},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & {{x}^{2}}+{{y}^{2}}=8 \\\\ & 2{{x}^{2}}-3{{y}^{2}}=1 \\\\ \\end{align} \\right.$ <br\/> <b> C\u00e2u 3: <\/b> H\u1ec7 c\u00f3 s\u1ed1 nghi\u1ec7m l\u00e0:","select":["A. M\u1ed9t nghi\u1ec7m ","B. Hai nghi\u1ec7m","C. Ba nghi\u1ec7m","D. B\u1ed1n nghi\u1ec7m "],"explain":"<span class='basic_left'> \u0110\u1eb7t $\\left\\{ \\begin{align} & {{x}^{2}}=X \\\\ & {{y}^{2}}=Y \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & X+Y=8 \\\\ & 2X-3Y=1 \\\\ \\end{align} \\right.$ <br\/> Theo c\u00e2u 1: $ \\left\\{ \\begin{align} & X=5 \\\\ & Y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & {{x}^{2}}=5 \\\\ & {{y}^{2}}=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\pm \\sqrt{5} \\\\ & y=\\pm \\sqrt{3} \\\\ \\end{align} \\right.$ <br\/> Suy ra $ S=\\left\\{ \\left( -\\sqrt{5};-\\sqrt{3} \\right);\\left( -\\sqrt{5};\\sqrt{3} \\right);\\left( \\sqrt{5};-\\sqrt{3} \\right);\\left( \\sqrt{5};\\sqrt{3} \\right) \\right\\}$ l\u00e0 t\u1eadp nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 b\u1ed1n nghi\u1ec7m ph\u00e2n bi\u1ec7t <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span>","column":4}]}],"id_ques":290}],"lesson":{"save":0,"level":2}}