{"segment":[{"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":[[["2"],["1"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align}& 2x-y=3 \\\\ & x+2y=4 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (_input_;_input_) ","hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf: T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, bi\u1ec3u di\u1ec5n $y$ theo $x$ ho\u1eb7c t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, bi\u1ec3u di\u1ec5n $x$ theo $y$ ","explain":"<span class='basic_left'> Ta c\u00f3: $\\left\\{ \\begin{align}& 2x-y=3 \\\\ & x+2y=4 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& y=2x-3\\,(1) \\\\ & x+2y=4\\,(2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y=2x-3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $x+2(2x-3)=4$$\\Leftrightarrow x+4x-6=4$$\\Leftrightarrow 5x=10$$\\Leftrightarrow x=2$ <br\/> Th\u1ebf $x=2$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: <br\/> $ y=2.2-3=1$ <br\/> Suy ra $\\left( 2;1 \\right)$ 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 $2$ v\u00e0 $1.$ <\/span><\/span>"}]}],"id_ques":251},{"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":[[["7"],["5"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align}& 5x+y=40 \\\\ & x+y=12 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (_input_;_input_) ","explain":"<span class='basic_left'><b>C\u00e1ch 1:<\/b> D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf: <br\/> Ta c\u00f3: $\\left\\{ \\begin{align}& 5x+y=40 \\\\ & x+y=12 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& y=40-5x\\,(1) \\\\ & x+y=12\\,(2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y = 40-5x$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $ x+40-5x=12$$\\Leftrightarrow -4x+40=12$$\\Leftrightarrow 4x=28$$\\Leftrightarrow x=7$ <br\/> Th\u1ebf $x=7$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: <br\/> $y=40-5.7$$=5$ <br\/> Suy ra $(7;5)$ 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 $7$ v\u00e0 $5.$ <\/span><br\/> <span class='basic_green'> Ch\u00fa \u00fd khi d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<\/span> <br\/>+ Khi h\u1ec7 s\u1ed1 c\u1ee7a m\u1ed9t \u1ea9n n\u00e0o \u0111\u00f3 trong m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 h\u1ec7 s\u1ed1 b\u1eb1ng $1$ ho\u1eb7c $-1$ th\u00ec ta n\u00ean d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<br\/>+ Trong c\u00e2u tr\u00ean, ta c\u00f3 th\u1ec3 r\u00fat $y$ \u1edf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t ho\u1eb7c th\u1ee9 hai. Ta c\u0169ng c\u00f3 th\u1ec3 r\u00fat $x$ \u1edf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai. <br\/><b> C\u00e1ch 2: <\/b> D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1<br\/>Tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau, ta \u0111\u01b0\u1ee3c:<br\/>$\\left\\{ \\begin{aligned} & 4x=28 \\\\ & x+y=12 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=7 \\\\ & x+y=12 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=7 \\\\ & 7+y=12 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=7 \\\\ & y=5 \\\\ \\end{aligned} \\right.$ <br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(7;5).$<br\/><span class='basic_green'>Ch\u00fa \u00fd khi d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1:<\/span><br\/>+ N\u1ebfu c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a c\u00f9ng m\u1ed9t \u1ea9n n\u00e0o \u0111\u00f3 trong hai ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng nhau th\u00ec ta tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau.<br\/>+ N\u1ebfu c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a c\u00f9ng m\u1ed9t \u1ea9n n\u00e0o \u0111\u00f3 trong hai ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ed1i nhau th\u00ec ta c\u1ed9ng t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau.<\/span>"}]}],"id_ques":252},{"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} & x-y=1 \\\\ & x+3y=9 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (_input_;_input_) ","hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf ho\u1eb7c ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1","explain":"<span class='basic_left'><b>C\u00e1ch 1:<\/b> Ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<br\/>T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta c\u00f3: $x=y+1$ (*)<br\/>Th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, ta \u0111\u01b0\u1ee3c:<br\/>$(y+1)+3y=9 \\Leftrightarrow 4y=8 \\Leftrightarrow y=2$ <br\/>Th\u1ebf $y=2$ v\u00e0o (*), ta \u0111\u01b0\u1ee3c: $x=2+1=3$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(3;2)$<br\/><b>C\u00e1ch 2:<\/b> Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1<br\/>Tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau, ta \u0111\u01b0\u1ee3c:<br\/>$\\begin{aligned} & \\,\\,\\,\\,\\,\\,\\,\\left\\{ \\begin{aligned} & 4y=8 \\\\ & x+3y=9 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=2 \\\\ & x+3.2=9 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=2 \\\\ & x=3 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ <br\/>V\u1eady $(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":253},{"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":[[["8"],["6"]]],"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}& -2x+4y=8 \\\\ & -x+3y=10 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (_input_;_input_) ","hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf: T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, bi\u1ec3u di\u1ec5n $x$ theo $y$ ","explain":"<span class='basic_left'> Ta c\u00f3: $\\left\\{ \\begin{align}& -2x+4y=8 \\\\ & -x+3y=10 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& -x+2y=4\\,(1) \\\\ & x=3y-10\\,(2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $x=3y-10$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: <br\/> $ -(3y-10)+2y=4$$\\Leftrightarrow -3y+10+2y=4$$\\Leftrightarrow -y+10=4$$\\Leftrightarrow y=6$ <br\/> Th\u1ebf $y=6$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: $x=3.6-10=8$ <br\/> Suy ra $\\left( 8;6 \\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 $8$ v\u00e0 $6.$ <\/span><br\/><b>C\u00e1ch kh\u00e1c: D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1:<\/b><br\/> Chia c\u1ea3 hai v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t cho $2$, ta \u0111\u01b0\u1ee3c: $\\left\\{ \\begin{aligned} & -x+2y=4 \\\\ & -x+3y=10 \\\\ \\end{aligned} \\right.$ <br\/>Tr\u1eeb t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai cho ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta \u0111\u01b0\u1ee3c:<br\/>$\\left\\{ \\begin{aligned} & y=6 \\\\ & -x+3y=10 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=6 \\\\ & -x+18=10 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=6 \\\\ & x=8 \\\\ \\end{aligned} \\right.$ <br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m l\u00e0 $\\left( 8;6 \\right)$<\/span>"}]}],"id_ques":254},{"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}{2}$;1)","B. ($\\dfrac{3}{2}$;1)","($-\\dfrac{1}{2}$;1)"],"ques":" T\u00ecm nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align}& 2x+5y=8 \\\\ & 2x-3y=0 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y) = $ (?;?) ","hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1: Tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau","explain":"<span class='basic_left'>Tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau, ta \u0111\u01b0\u1ee3c:<br\/>$\\left\\{ \\begin{aligned} & 8y=8 \\\\ & 2x=3y\\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=1 \\\\ & 2x=3y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=1 \\\\ & 2x=3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=1 \\\\ & x=\\dfrac{3}{2} \\\\ \\end{aligned} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m l\u00e0 $\\left(\\dfrac{3}{2};1 \\right)$<br\/> <\/span>"}]}],"id_ques":255},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 3x+y=5 \\\\ & 2x-y=5 \\\\ \\end{align} \\right.$ c\u00f3 nghi\u1ec7m $(x; y)$ l\u00e0:","select":["A. $(2;1)$ ","B. $(2;-1)$","C. $(1;2)$","D. $(-1;2)$"],"hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf: T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, bi\u1ec3u di\u1ec5n $y$ theo $x$","explain":"<span class='basic_left'> Ta c\u00f3: $\\left\\{ \\begin{align}& 3x+y=5 \\\\ & 2x-y=5 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & y=5-3x \\, (1) \\\\ & 2x-y=5 \\,(2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y=5-3x$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $2x-\\left( 5-3x \\right)=5$$\\Leftrightarrow 2x-5+3x=5$$\\Leftrightarrow 5x=10 \\Leftrightarrow x = 2$ <br\/> Th\u1ebf $x=2$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: $y= 5-3.2 = -1$ <br\/> Suy ra $(2;-1)$ 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 B. <\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span>Do h\u1ec7 s\u1ed1 c\u1ee7a \u1ea9n $y$ trong hai ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ed1i nhau n\u00ean d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1: C\u1ed9ng t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 s\u1ebd l\u00e0m m\u1ea5t \u1ea9n $y$<\/span>","column":2}]}],"id_ques":256},{"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 $(3; -1)$ c\u00f3 l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau kh\u00f4ng? <br\/> $\\left\\{ \\begin{align}& 3x+y=8 \\\\ & 7x-2y=23 \\\\ \\end{align} \\right.$","select":["A. C\u00f3","B. Kh\u00f4ng"],"hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho ho\u1eb7c thay tr\u1ef1c ti\u1ebfp c\u1eb7p s\u1ed1 $(3;-1)$ v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh xem c\u00f3 th\u1ecfa m\u00e3n hay kh\u00f4ng.","explain":"<span class='basic_left'>Ta c\u00f3: $\\left\\{ \\begin{align}& 3x+y=8 \\\\ & 7x-2y=23 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align}& y=8 - 3x\\, (1) \\\\ & 7x-2y=23 \\, (2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y = 8 - 3x$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/>$ 7x - 2(8-3x) = 23 \\Leftrightarrow 7x-16+6x = 23$ $\\Leftrightarrow 13x = 39 \\Leftrightarrow x = 3$ <br\/> Th\u1ebf $x = 3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: $y = 8- 3.3 = -1$ <br\/> Suy ra $(3; -1)$ 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 A.<\/span>","column":2}]}],"id_ques":257},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["-4"],["3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" C\u1eb7p s\u1ed1 n\u00e0o trong c\u00e1c c\u1eb7p s\u1ed1 $(-3; 4),\\, (-2; -6),\\, (-4; 3)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7: <br\/> $\\left\\{ \\begin{align}& x = y - 7 \\\\ & 3x + 4y = 0 \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> C\u1eb7p s\u1ed1 l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 (_input_;_input_) ","explain":"<span class='basic_left'> Th\u1ebf $x = y - 7$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $3x +4y = 0$, ta \u0111\u01b0\u1ee3c: <br\/>$ 3(y-7) + 4y = 0 \\Leftrightarrow 3y - 21 +4y = 0$ $ \\Leftrightarrow 7y = 21 \\Leftrightarrow y = 3$ <br\/> Th\u1ebf $y = 3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $x = y - 7$, ta \u0111\u01b0\u1ee3c: <br\/> $x = 3 - 7 = -4$ <br\/> V\u1eady $(-4; 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 $-4$ v\u00e0 $3.$<\/span> <br\/> <span class='basic_green'>Ch\u00fa \u00fd<\/span> <br\/> Ngo\u00e0i c\u00e1ch gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, h\u1ecdc sinh c\u00f3 th\u1ec3 thay tr\u1ef1c ti\u1ebfp c\u00e1c c\u1eb7p s\u1ed1 v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh xem c\u1eb7p s\u1ed1 n\u00e0o l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho."}]}],"id_ques":258},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"C\u1eb7p s\u1ed1 $\\left( \\dfrac{1}{3};\\dfrac{2}{3} \\right)$ kh\u00f4ng 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=1 \\\\ & 2x-y=0 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & 7x-3y=5 \\\\ & 4x+y=2 \\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align} & 3x+6y=5 \\\\ & x-2y=-1 \\\\ \\end{align} \\right.$"],"hint":"Gi\u1ea3i t\u1eebng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c thay tr\u1ef1c ti\u1ebfp c\u1eb7p s\u1ed1 $\\left( \\dfrac{1}{3};\\dfrac{2}{3} \\right)$ v\u00e0o t\u1eebng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh xem c\u00f3 th\u1ecfa m\u00e3n hay kh\u00f4ng.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $\\bullet\\left\\{ \\begin{align} & x+y=1 \\\\ & 2x-y=0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x+y=1\\,\\left( 1 \\right) \\\\ & y=2x\\,\\left( 2 \\right) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y=2x$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: <br\/> $x+2x=1\\Leftrightarrow 3x=1 $$\\Leftrightarrow x = \\dfrac{1}{3}$ <br\/> Th\u1ebf $x = \\dfrac{1}{3}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2)<br\/> $\\Rightarrow y=2. \\dfrac{1}{3} = \\dfrac{2}{3}$ <br\/> V\u1eady $\\left( \\dfrac{1}{3};\\dfrac{2}{3} \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\bullet\\left\\{ \\begin{align} & 7x-3y=5 \\\\ & 4x+y=2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 7x-3y=5\\,\\left( 3 \\right) \\\\ & y=2-4x\\, (4) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y=2-4x$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (3), ta \u0111\u01b0\u1ee3c: <br\/> $7x - 3.(2-4x)=5\\Leftrightarrow 7x-6+12x=5$ $\\Leftrightarrow 19x = 11 \\Leftrightarrow x = \\dfrac{11}{19}$ <br\/> Th\u1ebf $x = \\dfrac{11}{19}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (4), ta \u0111\u01b0\u1ee3c: <br\/> $ y= 2-4. \\dfrac{11}{19} = \\dfrac{-6}{19}$ <br\/> V\u1eady $\\left( \\dfrac{11}{19};\\dfrac{-6}{19} \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> Suy ra, $\\left( \\dfrac{1}{3};\\dfrac{2}{3} \\right)$ <b>kh\u00f4ng l\u00e0<\/b> nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\bullet\\left\\{ \\begin{align} & 3x+6y=5 \\\\ & x-2y=-1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 3x+6y=5\\,\\left( 5 \\right) \\\\ & x=2y-1\\,\\left( 6 \\right) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $x = 2y-1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (5), ta \u0111\u01b0\u1ee3c: <br\/> $3.(2y-1) + 6y = 5 \\Leftrightarrow 6y - 3 + 6y = 5 $ $\\Leftrightarrow 12y = 8 \\Leftrightarrow y =\\dfrac{2}{3} $ <br\/> Th\u1ebf $y = \\dfrac{2}{3}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (6), ta \u0111\u01b0\u1ee3c: <br\/> $ x = 2.\\dfrac{2}{3}-1 = \\dfrac{1}{3}$ <br\/> V\u1eady $\\left( \\dfrac{1}{3};\\dfrac{2}{3} \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span>","column":3}]}],"id_ques":259},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 6x-2y=8 \\\\ & 3x-y=3 \\\\ \\end{align} \\right.$ ","select":["A. H\u1ec7 c\u00f3 duy nh\u1ea5t nghi\u1ec7m ","B. H\u1ec7 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m","C. H\u1ec7 v\u00f4 nghi\u1ec7m","D. H\u1ec7 c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t"],"hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf \u0111\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c d\u1ef1a v\u00e0o minh h\u1ecda h\u00ecnh h\u1ecdc r\u1ed3i ch\u1ecdn \u0111\u00e1p \u00e1n","explain":"<span class='basic_left'> Ta c\u00f3: $\\left\\{ \\begin{align}& 6x-2y=8 \\\\ & 3x-y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& 6x-2y=8\\, (1) \\\\ & y=3x-3\\, (2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $y=3x-3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1) ta \u0111\u01b0\u1ee3c: <br\/> $6x-2(3x-3)=8$$\\Leftrightarrow 6x-6x+6=8$$\\Leftrightarrow 6=8$ (v\u00f4 l\u00ed) <br\/> V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span><br\/><span class='basic_green'><b>L\u01b0u \u00fd:<\/b><\/span> \u0110\u1ed1i v\u1edbi b\u00e0i to\u00e1n t\u00ecm s\u1ed1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n, ta c\u00f3 th\u1ec3 l\u00e0m theo hai c\u00e1ch:<br\/>C\u00e1ch 1: Gi\u1ea3i tr\u1ef1c ti\u1ebfp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>C\u00e1ch 2: D\u1ef1a v\u00e0o minh h\u1ecda h\u00ecnh h\u1ecdc (x\u00e9t v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi hai ph\u01b0\u01a1ng tr\u00ecnh trong h\u1ec7:<br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & ax+by=c \\\\ & a'x+b'y=c' \\\\ \\end{align} \\right.$ ($a,b,c,a\u2019,b\u2019,c\u2019$ kh\u00e1c $0$)<br\/>+ V\u00f4 nghi\u1ec7m n\u1ebfu $\\dfrac{a}{a'}=\\dfrac{b}{b'}\\ne \\dfrac{c}{c'}$<br\/> + V\u00f4 s\u1ed1 nghi\u1ec7m n\u1ebfu $\\dfrac{a}{a'}=\\dfrac{b}{b'}=\\dfrac{c}{c'}$<br\/>+ C\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t n\u1ebfu $\\dfrac{a}{a'}\\ne \\dfrac{b}{b'}$ <\/span>","column":2}]}],"id_ques":260},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $ a = \\dfrac{17}{10}; b = -\\dfrac{1}{10}$","B. $ a = -\\dfrac{17}{10}; b = \\dfrac{1}{10}$","C. $ a = -\\dfrac{17}{10}; b = -\\dfrac{1}{10}$"],"ques":" V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a $a,b$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 2x+by=a \\\\ & bx+ay=5 \\\\ \\end{align} \\right.$ nh\u1eadn $x=1, y=3$ l\u00e0 nghi\u1ec7m? <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $a=$ ?;$b=$ ?","hint":"Thay $x=1, y=3$ v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm $a;b$ ","explain":"<span class='basic_left'>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh nh\u1eadn $x=1, y=3$ l\u00e0 nghi\u1ec7m n\u00ean ta c\u00f3:<br\/>$\\left\\{ \\begin{align}& 2+3b=a\\,(1) \\\\ & b+3a=5\\, (2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $a=2+3b$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $b+3(2+3b)=5$$\\Leftrightarrow b+6+9b=5$$\\Leftrightarrow 10b=-1$$\\Leftrightarrow b=\\dfrac{-1}{10}$ <br\/> Th\u1ebf $b=\\dfrac{-1}{10}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: <br\/> $ a=2+3.\\left( \\dfrac{-1}{10} \\right)$$\\Leftrightarrow a=\\dfrac{17}{10}$ <br\/>"}]}],"id_ques":261},{"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"],["-1"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a $a,b$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 3ax+5y=b \\\\ & x+by=a \\\\ \\end{align} \\right.$ nh\u1eadn $x=1;y=-2$ l\u00e0 nghi\u1ec7m? <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(a;b) = $ (_input_;_input_) ","explain":"<span class='basic_left'>V\u00ec $x=1;$ $y=-2$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00ean ta c\u00f3: $\\left\\{ \\begin{align}& 3a-10=b\\,(1) \\\\ & 1-2b=a\\, (2) \\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $b=3a-10$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $1-2(3a-10)-a=0$$\\Leftrightarrow 1-6a+20-a=0$$\\Leftrightarrow 7a=21$$\\Leftrightarrow a=3$ <br\/> Th\u1ebf $a=3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: $ b=3.3-10=-1$<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $3$ v\u00e0 $-1.$ <\/span><\/span>"}]}],"id_ques":262},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2002"],["2001"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& mx-y=1 \\\\ & \\dfrac{x}{2}-\\dfrac{y}{3}=334 \\\\ \\end{align} \\right.$ (I)<br\/> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh khi $m = 1$ <\/b> <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x;y)=$ (_input_; _input_)","explain":"<span class='basic_left'> V\u1edbi $m=1$ th\u00ec (I) $\\Leftrightarrow \\left\\{ \\begin{align} & x-y=1 \\\\ & 3x-2y=2004 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=y+1\\,(1) \\\\ & 3x-2y=2004\\, (2)\\\\ \\end{align} \\right.$ <br\/> Th\u1ebf $x=y+1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2), ta \u0111\u01b0\u1ee3c: <br\/> $3(y+1)-2y=2004$$\\Leftrightarrow 3y+3-2y=2004$$\\Leftrightarrow y=2001$<br\/> Th\u1ebf $y=2001$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta \u0111\u01b0\u1ee3c: $ x=2001+1=2002$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $2002$ v\u00e0 $2001.$<\/span>"}]}],"id_ques":263},{"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 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& mx-y=1 \\\\ & \\dfrac{x}{2}-\\dfrac{y}{3}=334 \\\\ \\end{align} \\right.$ (I) <br\/> T\u00ecm $m$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m?","select":["A. $m\\ne\\dfrac{3}{2}$ ","B. $m\\ne - \\dfrac{3}{2}$","C. $m=\\dfrac{3}{2}$","D. $m=-\\dfrac{3}{2}$"],"hint":"H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m khi hai \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 song song v\u1edbi nhau","explain":"<span class='basic_left'>Ta c\u00f3: $\\left\\{ \\begin{align}& mx-y=1 \\\\ & \\dfrac{x}{2}-\\dfrac{y}{3}=334 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & mx-y=1 \\\\ & 3x-2y=2004 \\\\ \\end{align} \\right.$ <br\/> \u0110\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m th\u00ec hai \u0111\u01b0\u1eddng th\u1eb3ng $mx-y=1$ v\u00e0 $3x-2y=2004$ song song <br\/> $\\Leftrightarrow \\dfrac{m}{3}=\\dfrac{-1}{-2}\\ne \\dfrac{1}{2004}$$\\Leftrightarrow \\left\\{ \\begin{align} & 2m=3 \\\\ & m\\ne \\dfrac{3}{2004} \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow m=\\dfrac{3}{2}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C .<\/span>","column":4}]}],"id_ques":264},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 2x+3y=7 \\\\ & x+2y=4 \\\\ \\end{align} \\right.$ (1) v\u00e0 $\\left\\{ \\begin{align} & 2x+4y=8 \\\\ & x+y=3 \\\\ \\end{align} \\right.$ (2) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng \u0111\u00fang hay sai? ","select":["A. \u0110\u00fang ","B. Sai"],"hint":"Hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau n\u1ebfu ch\u00fang c\u00f3 c\u00f9ng t\u1eadp nghi\u1ec7m","explain":"<span class='basic_left'> Ta c\u00f3:<br\/> $\\left\\{ \\begin{align} & 2x+3y=7 \\\\ & x+2y=4 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 2x+3y=7\\, \\\\ & x=4-2y\\, \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align} & x=4-2y \\\\ & 2(4-2y)+3y=7 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=4-2.1 \\\\ & y=1 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=2 \\\\ & y=1 \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( 2;1 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (1) <br\/> $\\left\\{ \\begin{align} & 2x+4y=8 \\\\ & x+y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x+2y=4 \\\\ & x=3-y \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=3-y \\\\ & 3-y+2y=4 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=3-1 \\\\ & y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=2 \\\\ & y=1 \\\\ \\end{align} \\right.$ <br\/> Suy ra $\\left( 2;1 \\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (2) <br\/> T\u1eeb (1) v\u00e0 (2), suy ra hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 chung t\u1eadp nghi\u1ec7m<br\/>V\u1eady hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A .<\/span>","column":2}]}],"id_ques":265},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["5"],["-1"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'>T\u00ecm giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng $(d_1): 5x - 2y = c$ v\u00e0 $(d_2): x + by = 2,$ bi\u1ebft r\u1eb3ng $(d_1)$ \u0111i qua \u0111i\u1ec3m $A(5; -1)$ v\u00e0 $(d_2)$ \u0111i qua \u0111i\u1ec3m $B(-7; 3).$<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $(x; y)=$(_input_;_input_) ","hint":"Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $A$ v\u00e0 $B$ l\u1ea7n l\u01b0\u1ee3t v\u00e0o $(d_1)$ v\u00e0 $(d_2)$ \u0111\u1ec3 t\u00ecm $b$ v\u00e0 $c$ <br\/>T\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh x\u00e1c \u0111\u1ecbnh b\u1edfi ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.","explain":"<span class='basic_left'> Do $(d_1)$ \u0111i qua $A(5; -1)$ n\u00ean t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $A$ th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng $(d_1)$ <br\/> $\\Rightarrow 5.5 - 2.(-1) = c \\Leftrightarrow c = 27$ <br\/> $\\Rightarrow (d_1): 5x - 2y = 27$ <br\/> Do $(d_2)$ \u0111i qua $B(-7; 3)$ n\u00ean t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $B$ th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng $(d_2)$ <br\/> $\\Rightarrow -7 +3b = 2 \\Leftrightarrow 3b = 9 \\Leftrightarrow b = 3$ <br\/> $\\Rightarrow (d_2): x + 3y = 2$ <br\/> T\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a $(d_1)$ v\u00e0 $(d_2)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $\\left\\{ \\begin{align} & 5x-2y=27 \\\\ & x+3y=2 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 5x-2y=27 \\\\ & x=2-3y \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 5\\left( 2-3y \\right)-2y=27 \\\\ & x=2-3y \\\\ \\end{align} \\right.$ <br\/> $\\Leftrightarrow \\left\\{ \\begin{align} & 10-15y-2y=27 \\\\ & x=2-3y \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & 17y=-17 \\\\ & x=2-3y \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & y=-1 \\\\ & x=2-3.(-1) \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & y=-1 \\\\ & x=5 \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $5$ v\u00e0 $-1.$<\/span>"}]}],"id_ques":266},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["-5"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y=px+q$ \u0111i qua hai \u0111i\u1ec3m $E(-2;7)$ v\u00e0 $F(1;4).$ T\u00ednh $p.q$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $p.q=$ _input_","hint":"Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $E$ v\u00e0 $F$ l\u1ea7n l\u01b0\u1ee3t v\u00e0o h\u00e0m s\u1ed1 \u0111\u1ec3 t\u00ecm $p$ v\u00e0 $q.$","explain":"<span class='basic_left'> \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111i qua hai \u0111i\u1ec3m $E$ v\u00e0 $F$ n\u00ean ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\left\\{ \\begin{align} & 7=p.(-2)+q \\\\ & 4=p.1+q \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & q=2p+7 \\\\ & p+2p+7=4 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & q=2p+7 \\\\ & 3p=-3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & p=-1 \\\\ & q=5 \\\\ \\end{align} \\right.$ <br\/> V\u1edbi $p=-1; q=5$$\\Rightarrow p.q=-5$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $-5.$<\/span>"}]}],"id_ques":267},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"Kh\u00f4ng \u0111i\u1ec1n \u0111\u00e1p \u00e1n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1","temp":"fill_the_blank_random","correct":[[["0,5"],["-3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y=ux+v$ \u0111i qua hai \u0111i\u1ec3m $P(-4;-5)$ v\u00e0 $Q(2;-2).$ T\u00ednh $u$ v\u00e0 $v.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $u=$ _input_;$v=$_input_","explain":"<span class='basic_left'> \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111i qua hai \u0111i\u1ec3m $P$ v\u00e0 $Q$ n\u00ean ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\left\\{ \\begin{align} & -5=u.(-4)+v \\\\ & -2=u.2+v \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & v=4u-5 \\\\ & 2u+4u-5=-2 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & v=4u-5 \\\\ & 6u=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & u=\\dfrac{1}{2} \\\\ & v=-3 \\\\ \\end{align} \\right.$ <br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $0,5;$ $-3.$<\/span>"}]}],"id_ques":268},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x-2y=6 \\\\ & -\\frac{1}{2}x+y=-3 \\\\ \\end{align} \\right.$ <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. H\u1ec7 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m ","B. H\u1ec7 v\u00f4 nghi\u1ec7m","C. H\u1ec7 c\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t ","D. H\u1ec7 c\u00f3 hai nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t "],"explain":"<span class='basic_left'>Ta c\u00f3: $\\left\\{ \\begin{align} & x-2y=6 \\\\ & -\\frac{1}{2}x+y=-3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=6+2y \\\\ & -\\frac{1}{2}(6+2y)+y=-3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=6+2y \\\\ & 0y=0 \\\\ \\end{align} \\right.$ <br\/> Suy ra h\u1ec7 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span> <br\/> <span class='basic_green'> Ch\u00fa \u00fd:<\/span> <br\/> Trong qu\u00e1 tr\u00ecnh gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf, ta th\u1ea5y xu\u1ea5t hi\u1ec7n ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng $0x=b$ <br\/> $\\bullet $ N\u1ebfu $b= 0$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m <br\/> $\\bullet $ V\u00e0 $b \\ne 0$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m.<\/span><\/span>","column":2}]}],"id_ques":269},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Trong c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh sau, ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o v\u00f4 nghi\u1ec7m? ","select":["A. $\\left\\{ \\begin{align} & x+y=1 \\\\ & x-y=1 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & 3x-2y=5 \\\\ & 2x+y=1 \\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align} & -x+2y=3 \\\\ & 2x-y=3 \\\\ \\end{align} \\right.$","D. $\\left\\{ \\begin{align}& x-y=1 \\\\ & 2x-2y=3 \\\\ \\end{align} \\right.$ "],"explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\bullet\\left\\{ \\begin{align} & x+y=1 \\\\ & x-y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1+y \\\\ & 1+y+y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & y=0 \\\\ \\end{align} \\right.$ <br\/> Suy ra h\u1ec7 c\u00f3 duy nh\u1ea5t nghi\u1ec7m <br\/> $\\bullet\\left\\{ \\begin{align} & 3x-2y=5 \\\\ & 2x+y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=1-2x \\\\ & 3x-2(1-2x)=5 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=1-2x \\\\ & 7x=7 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & y=-1 \\\\ \\end{align} \\right.$ <br\/> Suy ra h\u1ec7 c\u00f3 duy nh\u1ea5t nghi\u1ec7m <br\/> $\\bullet\\left\\{ \\begin{align} & -x+2y=3 \\\\ & 2x-y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=2y-3 \\\\ & 2(2y-3)-y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=2y-3 \\\\ & 3y=9 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=3 \\\\ & y=3 \\\\ \\end{align} \\right.$ <br\/> Suy ra h\u1ec7 c\u00f3 duy nh\u1ea5t nghi\u1ec7m <br\/> $\\bullet\\left\\{ \\begin{align} & x-y=1 \\\\ & 2x-2y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1+y \\\\ & 2(1+y)-2y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=1+y \\\\ & 0y=1\\, (\\text {v\u00f4 nghi\u1ec7m}) \\\\ \\end{align} \\right.$ <br\/> Suy ra h\u1ec7 v\u00f4 nghi\u1ec7m <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span> ","column":2}]}],"id_ques":270}],"lesson":{"save":0,"level":1}}