{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"C\u1eb7p s\u1ed1 $(1;1)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh: ","select":["A. $2x-y=1$","B. $x-y=2$","C. $x+3y=-3$","D. $5x-2y=7$"],"hint":"Thay $(1;1)$ v\u00e0o t\u1eebng ph\u01b0\u01a1ng tr\u00ecnh xem n\u00f3 th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o","explain":" <span class='basic_left'> $\\bullet$ Thay $x=1;y=1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $2x-y=1$ ta \u0111\u01b0\u1ee3c: <br\/> $2.1-1=1$ <br\/> V\u1eady $(1;1)$ <b> l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $2x-y=1$ <br\/> $\\bullet$ Thay $x=1;y=1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $x-y=2$ ta \u0111\u01b0\u1ee3c: <br\/> $1-1=0\\ne 2$ <br\/> V\u1eady $(1;1)$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $x-y=2$ <br\/> $\\bullet$ Thay $x=1;y=1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $x+3y=-3$ ta \u0111\u01b0\u1ee3c: <br\/> $1+3.1=4\\ne -3$ <br\/> V\u1eady $(1;1)$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $x+3y=-3$ <br\/> $\\bullet$ Thay $x=1;y=1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $5x-2y=7$ ta \u0111\u01b0\u1ee3c: <br\/> $5.1-2.1=3\\ne 7$ <br\/> V\u1eady $(1;1)$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $5x-2y=7$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span>","column":4}]}],"id_ques":221},{"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 $(3;-11)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh: ","select":["A. $9,6x+y=10,8$","B. $3,2x-y=20,6$","C. $6,9x+11y=10,3$","D. $3,2x-2,3y=17,5$"],"explain":" <span class='basic_left'> $\\bullet$ Thay $x=3;y=-11$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $9,6x+y=10,8$ ta \u0111\u01b0\u1ee3c: <br\/> $9,6.3+(-11)=17,8\\ne10,8$ <br\/> V\u1eady $(3;-11)$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $9,6x+y=10,8$ <br\/> $\\bullet$ Thay $x=3;y=-11$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $3,2x-y=20,6$ ta \u0111\u01b0\u1ee3c: <br\/> $3,2.3-(-11)=20,6$ <br\/> V\u1eady $(3;-11)$ <b> l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $3,2x-y=20,6$ <br\/> $\\bullet$ Thay $x=3;y=-11$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $6,9x+11y=10,3$ ta \u0111\u01b0\u1ee3c: <br\/> $6,9.3+11.(-11)=100,3\\ne10,3$ <br\/> V\u1eady $(3;-11)$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $6,9x+11y=10,3$ <br\/> $\\bullet$ Thay $x=3;y=-11$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $3,2x-2,3y=17,5$ ta \u0111\u01b0\u1ee3c: <br\/> $3,2.3-2,3.(-11)=34,9\\ne 17,5$ <br\/> V\u1eady $(3;-11)$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $3,2x-2,3y=17,5$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span>","column":2}]}],"id_ques":222},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Hai ph\u01b0\u01a1ng tr\u00ecnh $5x+3y=7$ v\u00e0 $2x+2y=3$ c\u00f3 c\u00f9ng t\u1eadp nghi\u1ec7m \u0111\u00fang hay sai?","select":["A. \u0110\u00fang","B. Sai"],"explain":" <span class='basic_left'> Cho $x$ l\u00e0 gi\u00e1 tr\u1ecb b\u1ea5t k\u00ec, ta c\u00f3 $5x+3y=7$$\\Leftrightarrow y=\\dfrac{-5}{3}x+\\dfrac{7}{3}$ <br\/> Suy ra t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0: $S=\\left\\{\\left(x;\\dfrac{-5}{3}x+\\dfrac{7}{3}\\right) | x\\in\\mathbb{R}\\right\\}$ <br\/> Cho $x$ l\u00e0 gi\u00e1 tr\u1ecb b\u1ea5t k\u00ec, ta c\u00f3 $2x+2y=3$$\\Leftrightarrow 2y=-2x+3$ $\\Leftrightarrow y=-x+\\dfrac{3}{2}$<br\/> Suy ra t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0: $S=\\left\\{\\left(x;-x+\\dfrac{3}{2}\\right) | x\\in\\mathbb{R}\\right\\}$ <br\/> V\u1eady hai ph\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng c\u00f3 c\u00f9ng t\u1eadp nghi\u1ec7m <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span>","column":2}]}],"id_ques":223},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"X\u00e9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& ax+by=c \\\\ & a'x+b'y=c' \\\\ \\end{align} \\right.$ (I) <br\/> H\u1ec7 (I) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m khi:","select":["A. $\\dfrac{a}{a'}\\ne \\dfrac{b}{b'}$","B. $\\dfrac{a}{a'}= \\dfrac{b}{b'}$","C. $\\dfrac{a}{a'}= \\dfrac{b}{b'}=\\dfrac{c}{c'}$","D. $\\dfrac{a}{a'}= \\dfrac{b}{b'}\\ne\\dfrac{c}{c'}$"],"explain":" <span class='basic_left'> \u0110\u1ec3 h\u1ec7 (I) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m th\u00ec hai \u0111\u01b0\u1eddng th\u1eb3ng $ax+by=c$ v\u00e0 $a'x+b'y=c'$ tr\u00f9ng nhau <br\/> $\\Leftrightarrow \\dfrac{a}{a'}= \\dfrac{b}{b'}= \\dfrac{c}{c'}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C <\/span>","column":2}]}],"id_ques":224},{"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":" T\u00ecm $k$ \u0111\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau t\u01b0\u01a1ng \u0111\u01b0\u01a1ng? (I) $\\left\\{ \\begin{align}& 5x=14 \\\\ & 2x - 7y=5\\\\ \\end{align} \\right.;$ (II) $\\left\\{ \\begin{align}& 3x+7y =9 \\\\ & 2x-7y=k \\\\ \\end{align} \\right.$ <br\/><br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $k = $ _input_ ","hint":"H\u1ec7 hai 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'> Ta c\u00f3: (I) $\\Leftrightarrow \\left\\{ \\begin{align}& x=\\dfrac{14}{5} \\\\ & 2.\\dfrac{14}{5}-7.y=5 \\\\ \\end{align} \\right.$$\\Leftrightarrow\\left\\{ \\begin{align}& x=\\dfrac{14}{5} \\\\ & y=\\dfrac{3}{35} \\\\ \\end{align} \\right.$ <br\/> \u0110\u1ec3 h\u1ec7 (I) v\u00e0 (II) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng n\u1ebfu v\u00e0 ch\u1ec9 n\u1ebfu ch\u00fang c\u00f3 chung t\u1eadp nghi\u1ec7m <br\/> Suy ra $\\left(\\dfrac{14}{5}; \\dfrac{3}{35} \\right)$ c\u0169ng l\u00e0 nghi\u1ec7m c\u1ee7a (II) <br\/> Thay $x=\\dfrac{14}{5};y=\\dfrac{3}{35}$ v\u00e0o (II) <br\/> $\\left\\{ \\begin{align}& 3.\\dfrac{14}{5}+7.\\dfrac{3}{35}=9\\, \\text{(\u0111\u00fang)} \\\\ & 2.\\dfrac{14}{5}-7.\\dfrac{3}{35}=k(*) \\\\ \\end{align} \\right.$ <br\/> $(*)\\Leftrightarrow \\dfrac{28}{5}-\\dfrac{21}{35} = k$ $\\Leftrightarrow k=5$<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $5$<\/span>"}]}],"id_ques":225},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm $n$ \u0111\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau t\u01b0\u01a1ng \u0111\u01b0\u01a1ng? (I) $\\left\\{ \\begin{align}& \\dfrac{x}{2}-\\dfrac{y}{3}=1 \\\\ & 5x-8y=3\\\\ \\end{align} \\right.;$ (II) $\\left\\{ \\begin{align}& 3x-2y=n \\\\ & \\dfrac{5}{4}x-2y=\\dfrac{3}{4} \\\\ \\end{align} \\right.$ <br\/><br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $n = $ _input_ ","hint":"T\u00ecm h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng b\u1eb1ng c\u00e1ch bi\u1ebfn \u0111\u1ed5i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) v\u1ec1 (II)","explain":" <span class='basic_left'> Ta c\u00f3: $\\dfrac{x}{2}-\\dfrac{y}{3}=1$ $\\Leftrightarrow 3x-2y=6$ <br\/> Chia c\u1ea3 hai v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $5x-8y=3$ cho $4$ ta \u0111\u01b0\u1ee3c: $\\dfrac{5}{4}x-2y=\\dfrac{3}{4}$ <br\/> V\u1eady $\\left\\{ \\begin{align}& \\dfrac{x}{2}-\\dfrac{y}{3}=1 \\\\ & 5x-8y=3\\\\ \\end{align} \\right.$$\\Leftrightarrow\\left\\{ \\begin{align}& 3x-2y=6 \\\\ & \\dfrac{5}{4}x-2y=\\dfrac{3}{4} \\\\ \\end{align} \\right.$ <br\/> Suy ra $n=6$ th\u00ec hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $6$<\/span>"}]}],"id_ques":226},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"\u0110\u01b0\u1eddng th\u1eb3ng $\\sqrt{5}x-y=\\sqrt{5}\\left( \\sqrt{3}-1 \\right)$ \u0111i qua \u0111i\u1ec3m: ","select":["A. $M\\left( \\sqrt{3}-1;0 \\right)$","B. $N\\left( -\\sqrt{5}\\left( \\sqrt{3}-1 \\right);0 \\right)$","C. $P\\left( 0;\\sqrt{3}-1 \\right) $ ","D. $Q\\left( 0;\\sqrt{5}\\left( \\sqrt{3}-1 \\right) \\right)$"],"explain":" <span class='basic_left'> <span class='basic_left'> $\\bullet$ Thay $y= 0$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $\\sqrt{5}x-y=\\sqrt{5}\\left( \\sqrt{3}-1 \\right)$ ta \u0111\u01b0\u1ee3c: <br\/> $\\sqrt{5}.x-0=\\sqrt{5}\\left( \\sqrt{3}-1 \\right)$ $\\Leftrightarrow x=\\left( \\sqrt{3}-1 \\right)$<br\/> V\u1eady $M$ <b> l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\,\\,\\,\\,\\,\\,\\,N$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh <br\/> $\\bullet$ Thay $x= 0$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $\\sqrt{5}x-y=\\sqrt{5}\\left( \\sqrt{3}-1 \\right)$ ta \u0111\u01b0\u1ee3c: <br\/> $\\sqrt{5}.0-y=\\sqrt{5}\\left( \\sqrt{3}-1 \\right)$ $\\Leftrightarrow y=-\\sqrt{5}\\left( \\sqrt{3}-1 \\right)$<br\/> V\u1eady $P, Q$ <b> kh\u00f4ng l\u00e0 <\/b> nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":227},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x-y=4 \\\\ & -2017x-2017y=0 \\\\ \\end{align} \\right.$ c\u00f3 nghi\u1ec7m l\u00e0 $\\left\\{ \\begin{align}& x=2 \\\\ & y=-2 \\\\ \\end{align} \\right..$ <br\/> <br\/> Kh\u1eb3ng \u0111\u1ecbnh tr\u00ean \u0111\u00fang hay sai? ","select":["A. \u0110\u00fang","B. Sai"],"explain":" <span class='basic_left'> Thay $x= 2;y=-2$ v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x-y=4 \\\\ & -2017x-2017y=0 \\\\ \\end{align} \\right.$ ta \u0111\u01b0\u1ee3c: <br\/><br\/> $\\left\\{ \\begin{align}& 2-(-2)=4 \\\\ & -2017.2-2017.(-2)=0 \\\\ \\end{align} \\right.$ (\u0111\u00fang) <br\/><br\/> V\u1eady $\\left\\{ \\begin{align}& x=2 \\\\ & y=-2 \\\\ \\end{align} \\right.$ <b> l\u00e0 <\/b> 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":228},{"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":[[["-15"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $b$ \u0111\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng $2x-y=5$ v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng $x+3y = b$ c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m tr\u00ean tr\u1ee5c tung. <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $ b =$ _input_","explain":" <span class='basic_left'> Ta c\u00f3: $2x-y=5$ $\\Leftrightarrow y=2y-5$ $(d)$<br\/> $x+3y=b$ $\\Leftrightarrow y=\\dfrac{-1}{3}x+\\dfrac{b}{3}$ $(d')$ <br\/> \u0110\u1ec3 hai \u0111\u01b0\u1eddng th\u1eb3ng $(d)$ v\u00e0 $(d')$ c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m tr\u00ean tr\u1ee5c tung th\u00ec tung \u0111\u1ed9 g\u00f3c c\u1ee7a ch\u00fang b\u1eb1ng nhau <br\/> $\\Leftrightarrow -5=\\dfrac{b}{3}$$\\Leftrightarrow b = -15$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $-15$ <\/span>"}]}],"id_ques":229},{"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}$","B. $\\dfrac{1}{3}$","C. $\\dfrac{1}{4}$"],"ques":"T\u00ecm $m$ \u0111\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng $x+y=m$ v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng $3x+2y=1$ c\u1eaft nhau tr\u00ean tr\u1ee5c ho\u00e0nh. <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $ m =$ ?","explain":" <span class='basic_left'> <span class='basic_left'>Cho $y=0,$ ta c\u00f3: <br\/> $x+y=m$ $\\Leftrightarrow x=m$ <br\/> Cho $y=0,$ ta c\u00f3: <br\/> $3x+2y=1$ $\\Leftrightarrow x=\\dfrac{1}{3}$ <br\/> \u0110\u1ec3 hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau tr\u00ean tr\u1ee5c ho\u00e0nh <br\/> $\\Leftrightarrow m = \\dfrac{1}{3}$ <br\/><\/span>"}]}],"id_ques":230},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\dfrac{5}{2}$","B. $\\dfrac{5}{3}$","C. $\\dfrac{5}{4}$"],"ques":"T\u00ecm $m$ \u0111\u1ec3 hai \u0111\u01b0\u1eddng th\u1eb3ng $mx+3y=10$ v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh $x-2y=4$ c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m tr\u00ean tr\u1ee5c ho\u00e0nh. <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $ m =$ ?","explain":" <span class='basic_left'> <span class='basic_left'>Cho $y=0,$ ta c\u00f3: <br\/> $mx+3y=10$ $\\Leftrightarrow mx=10$ $\\Leftrightarrow x=\\dfrac{10}{m}$ <br\/> Cho $y=0,$ ta c\u00f3: <br\/> $x-2y=4$ $\\Leftrightarrow x=4$ <br\/> \u0110\u1ec3 hai ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 chung nghi\u1ec7m $x$ <br\/> $\\Leftrightarrow \\dfrac{10}{m} = 4$ $\\Leftrightarrow m =\\dfrac{5}{2}$ <br\/> <\/span>"}]}],"id_ques":231},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["9"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" N\u1ebfu \u0111i\u1ec3m $B(1;2)$ thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng $kx+(k-1)y=2k+7$ th\u00ec $k = $ _input_ ","explain":" <span class='basic_left'> Do $B(1;2)$ thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng $kx+(k-1)y=2k+7$ n\u00ean t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $B$ th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh <br\/>Thay $x=1;y=2$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: <br\/> $k.1+(k-1).2$$=2k+7$ <br\/> $\\Leftrightarrow k+2k-2=2k+7$ <br\/> $\\Leftrightarrow k=9$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $9$<\/span>"}]}],"id_ques":232},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $-\\dfrac{11}{8}$","B. $\\dfrac{11}{8}$","C. $\\dfrac{-10}{8}$","D. $\\dfrac{10}{8}$"],"ques":"N\u1ebfu \u0111i\u1ec3m $C(-2;-3)$ thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng $nx+(n+2)y=3n+5$ th\u00ec $ n =$ ?","explain":" <span class='basic_left'>Do $C(-2;-3)$ thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng $nx+(n+2)y=3n+5$ n\u00ean t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m $C$ th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh <br\/> Thay $x=-2;y=-3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: <br\/> $n.(-2)+(n+2).(-3)=3n+5$ <br\/> $\\Leftrightarrow -2n-3n-6=3n+5$ <br\/> $\\Leftrightarrow 8n=-11$ <br\/>$\\Leftrightarrow n=\\dfrac{-11}{8}$ <br\/>"}]}],"id_ques":233},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"\u0110\u01b0\u1eddng th\u1eb3ng $d$ bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $-0,01x-0,01y=0,02$ l\u00e0: ","select":["A. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai14/lv2/img\/H931_TB5.png' \/><\/center>","B. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai14/lv2/img\/H931_TB6.png' \/><\/center>","C. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai14/lv2/img\/H931_TB7.png' \/><\/center>"],"explain":" <span class='basic_left'> Thay $x=0$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $-0,01x-0,01y=0,02$ ta \u0111\u01b0\u1ee3c: <br\/> $-0,01.0-0,01y=0,02$ $\\Leftrightarrow y = -2$ <br\/> V\u1eady $(0;-2)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $-0,01x-0,01y=0,02$ <br\/> Thay $y=0$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $-0,01x-0,01y=0,02$ ta \u0111\u01b0\u1ee3c: <br\/> $-0,01x-0,01.0=0,02$ $\\Leftrightarrow x=-2$ <br\/> V\u1eady $(-2;0)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $-0,01x-0,01y=0,02$ <br\/> Suy ra \u0111\u01b0\u1eddng th\u1eb3ng bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u0111i qua hai \u0111i\u1ec3m $(0;-2)$ v\u00e0 $(-2;0)$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span>","column":3}]}],"id_ques":234},{"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":[[["4"],["1"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"X\u00e1c \u0111\u1ecbnh $m,n$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& mx+3y=6 \\\\ & 2x+ny=4 \\\\ \\end{align} \\right.$ c\u00f3 nghi\u1ec7m $(x,y) =(3;-2)$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $m=$ _input_; $n=$_input_","explain":" <span class='basic_left'> Thay $x=3;y=-2$ v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: <br\/> $\\left\\{ \\begin{align}& m.3+3.(-2)=6 \\\\ & 2.3+n.(-2)=4 \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align}& 3m-6=6 \\\\ & 6-2n=4 \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align}& 3m=12 \\\\ & 2n=2\\dfrac{-10}{3} \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align}& m=4 \\\\ & n=1 \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $4$ v\u00e0 $1$ <\/span>"}]}],"id_ques":235},{"time":24,"part":[{"time":3,"title":"N\u1ed1i m\u1ed7i c\u1eb7p s\u1ed1 \u1edf c\u1ed9t A v\u00e0 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh \u1edf c\u1ed9t B sao cho c\u1eb7p s\u1ed1 n\u00e0y l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3","audio":"","temp":"matching","correct":[["2","3","1"]],"list":[{"point":5,"left":["$(4;-3)$","$(3;-2)$","$(6;1)$"],"right":["$x-5y=1$","$3x+5y=-3$","$7x-0y=21$"],"top":100,"explain":" <span class='basic_left'> Thay $x=4;y=-3$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $3x+5y=-3,$ ta \u0111\u01b0\u1ee3c: <br\/> $3.4+5.(-3)=-3$ <br\/> V\u1eady $(4;-3)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $3x+5y=-3$ <br\/> Thay $x=3;y=-2$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $7x-0y=21,$ ta \u0111\u01b0\u1ee3c: <br\/> $7.3-0.(-2)=21$ <br\/> V\u1eady $(3;-2)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $7x-0y=21$<br\/> Thay $x=6;y=1$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $x-5y=1,$ ta \u0111\u01b0\u1ee3c: <br\/> $6-5.1=1$ <br\/> V\u1eady $(6;1)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $x-5y=1$"}]}],"id_ques":236},{"time":24,"part":[{"time":3,"title":"N\u1ed1i m\u1ed7i ph\u01b0\u01a1ng tr\u00ecnh \u1edf c\u1ed9t A v\u00e0 m\u1ed9t c\u1eb7p s\u1ed1 \u1edf c\u1ed9t B sao cho \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y \u0111i qua \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 l\u00e0 c\u1eb7p s\u1ed1 \u0111\u00e3 cho","audio":"","temp":"matching","correct":[["3","2","1"]],"list":[{"point":5,"left":["$x=y-2$","$2x+3y=-6$","$0x+12y=0$"],"right":["$(999;0)$","$\\left(-1;-\\dfrac{4}{3}\\right)$","$(5;7)$"],"top":100,"hint":"\u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y \u0111i qua \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 l\u00e0 c\u1eb7p s\u1ed1 \u0111\u00e3 cho n\u1ebfu c\u1eb7p s\u1ed1 l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh","explain":" <span class='basic_left'> Thay $x=5;y=7$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $x=y-2,$ ta \u0111\u01b0\u1ee3c: <br\/> $5=7-2$ $\\Leftrightarrow 5=5$<br\/> V\u1eady $(5;7)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $x=y-2$ <br\/> Thay $x=-1;y=-\\dfrac{4}{3}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $2x+3y=-6,$ ta \u0111\u01b0\u1ee3c: <br\/> $2.(-1)+3.(-\\dfrac{4}{3})=-6$ <br\/> V\u1eady $\\left(-1;-\\dfrac{4}{3}\\right)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $2x+3y=-6$ <br\/> Thay $x=999;y=0$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh $0x+12y=0,$ ta \u0111\u01b0\u1ee3c: <br\/> $0.999+12.0=0$ <br\/> V\u1eady $(999;0)$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $0x+12y=0$"}]}],"id_ques":237},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 $Oxy$, t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $-\\sqrt{3}x+\\sqrt{3}y=0$ \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ecb b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng:","select":["A. \u0110i qua \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 $(1;1)$ v\u00e0 song song v\u1edbi tr\u1ee5c ho\u00e0nh","B. \u0110i qua hai \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 $(0;0)$ v\u00e0 $(-1; 1)$","C. \u0110i qua hai \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 $(0;1)$ v\u00e0 $(1;-1)$","D. L\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $xOy$"],"explain":" <span class='basic_left'> V\u1edbi $x$ b\u1ea5t k\u00ec ($x\\in \\mathbb{R}$), ta c\u00f3: <br\/> $-\\sqrt{3}x+\\sqrt{3}y=0$ $\\sqrt{3}y=\\sqrt{3}x$ $\\Leftrightarrow y=x\\, (d)$ <br\/> V\u1edbi $x = 1\\Rightarrow y=1;$ v\u1edbi $x=0\\Rightarrow y=0$ <br\/> Suy ra $(d)$ \u0111i qua hai \u0111i\u1ec3m $(1;1)$ v\u00e0 $(0;0)$ <br\/> Suy ra \u0111\u00e1p \u00e1n A, B, C kh\u00f4ng \u0111\u00fang <br\/> G\u1ecdi $\\alpha$ l\u00e0 g\u00f3c t\u1ea1o b\u1edfi $(d)$ v\u00e0 $Ox$, ta c\u00f3: <br\/> $tan \\alpha = a = 1$ <br\/> $\\Rightarrow \\alpha = 45^o$ <br\/> V\u1eady $(d)$ l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $xOy$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span>","column":1}]}],"id_ques":238},{"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":[[["-20"],["-9"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $m,n$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 3x+5y=m \\\\ & nx-15y=60 \\\\ \\end{align} \\right.$ (*) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $ m =$ _input_;$n=$_input_","hint":"Xem l\u1ea1i \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 h\u1ec7 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m","explain":" <span class='basic_left'> \u0110\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m <br\/> $\\Rightarrow \\dfrac{3}{n}=\\dfrac{5}{-15}=\\dfrac{m}{60}=\\dfrac{-1}{3}$$\\Leftrightarrow \\left\\{ \\begin{align}& \\dfrac{3}{n}=\\dfrac{-1}{3} \\\\ & \\dfrac{m}{60}=\\dfrac{-1}{3} \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align}& n=-9 \\\\ & m=-20 \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $-20$ v\u00e0 $-9$ <\/span>"}]}],"id_ques":239},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 $Oxy$, t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $2x-y-1=0$ (*) \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m $M$ v\u00e0 $N$ c\u00f3 t\u1ecda \u0111\u1ed9:","select":["A. $M(0;-1)$ v\u00e0 $N\\left(0;\\dfrac{1}{2}\\right)$","B. $M(0;1)$ v\u00e0 $N\\left(-\\dfrac{1}{2};0\\right)$","C. $M(0;1)$ v\u00e0 $N\\left(\\dfrac{1}{2};0\\right)$","D. $M(0;-1)$ v\u00e0 $N\\left(\\dfrac{1}{2};0\\right)$"],"hint":"T\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng (*) v\u1edbi hai tr\u1ee5c t\u1ecda \u0111\u1ed9","explain":" <span class='basic_left'> Thay $x = 0$ v\u00e0o (*) ta \u0111\u01b0\u1ee3c: <br\/> $2.0 - y - 1 = 0\\Leftrightarrow y = -1$ <br\/> $\\Rightarrow M(0; -1)$ thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng (*) <br\/> Thay $y = 0$ v\u00e0o (*) ta \u0111\u01b0\u1ee3c: <br\/> $2.x - 0 - 1 = 0\\Leftrightarrow 2x = 1 \\Leftrightarrow x = \\dfrac{1}{2}$ <br\/> $\\Rightarrow N\\left(\\dfrac{1}{2};0\\right)$ thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng (*) <br\/> V\u1eady \u0111\u01b0\u1eddng th\u1eb3ng bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (*) \u0111i qua hai \u0111i\u1ec3m $M(0;-1)$ v\u00e0 $N\\left(\\dfrac{1}{2};0\\right)$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span>","column":2}]}],"id_ques":240}],"lesson":{"save":0,"level":2}}