{"segment":[{"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":"\u0110o\u00e1n s\u1ed1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align} & 2x+y=3 \\\\ & 3x-y=1 \\\\ \\end{align} \\right.$","select":["A. C\u00f3 1 nghi\u1ec7m duy nh\u1ea5t","B. V\u00f4 nghi\u1ec7m","C. V\u00f4 s\u1ed1 nghi\u1ec7m"],"hint":"D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p 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.","explain":"<span class='basic_left'>X\u00e9t hai \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 \u0111\u00e3 cho: $2x+y=3$ v\u00e0 $3x-y=1$<br\/>V\u00ec $\\dfrac{2}{3}\\ne \\dfrac{1}{-1}$ n\u00ean hai \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00e3 cho c\u1eaft nhau. <br\/>Suy ra h\u1ec7 c\u00f3 1 nghi\u1ec7m duy nh\u1ea5t<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<br\/><\/span><b> C\u00e1ch 2:<\/b> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1<br\/>$\\left\\{ \\begin{aligned} & 2x+y=3 \\\\ & 3x-y=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 5x=4 \\\\ & y=3x-1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=\\dfrac{4}{5} \\\\ & y=3.\\dfrac{4}{5}-1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=\\dfrac{4}{5} \\\\ & y=\\dfrac{7}{5} \\\\ \\end{aligned} \\right.$<br\/>V\u1eady h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $\\left(\\dfrac{4}{5}; \\dfrac{7}{5}\\right)$.<br\/>Tuy nhi\u00ean v\u1edbi b\u00e0i to\u00e1n ch\u1ec9 \u0111o\u00e1n s\u1ed1 nghi\u1ec7m m\u00e0 kh\u00f4ng y\u00eau c\u1ea7u t\u00ecm nghi\u1ec7m th\u00ec ta d\u00f9ng c\u00e1ch 1 s\u1ebd nhanh h\u01a1n.<\/span>","column":3}]}],"id_ques":351},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"],["2"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{aligned} & x+y=4 \\\\ & 4x-3y=2 \\\\ \\end{aligned} \\right.$ <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m l\u00e0 (_input_;_input_)","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>Gi\u1ea3i h\u1ec7 b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf: T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, bi\u1ec3u di\u1ec5n $x$ theo $y$ r\u1ed3i th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3<br\/>$\\left\\{ \\begin{aligned} & x+y=4 \\\\ & 4x-3y=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=4-y \\\\ & 4\\left( 4-y \\right)-3y=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=4-y \\\\ & 16-4y-3y=2 \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=4-y \\\\ & -7y=-14 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=4-y \\\\ & y=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=2 \\\\ & y=2 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(2;2)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2$ v\u00e0 $2$<\/span><\/span>"}]}],"id_ques":352},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{aligned} & 2x-3y=1 \\\\ & x+3y=2 \\\\ \\end{aligned} \\right.$ l\u00e0: ","select":["A. $\\left(\\dfrac{1}{3};1 \\right)$","B. $\\left(1;\\dfrac{1}{3} \\right)$","C. $(3;1)$","D. $(1;3)$"],"hint":"","explain":"<span class='basic_left'>T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, bi\u1ec3u di\u1ec5n $x$ theo $y$ r\u1ed3i th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta c\u00f3:<br\/>$\\left\\{ \\begin{aligned} & 2x-3y=1 \\\\ & x+3y=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2x-3y=1 \\\\ & x=2-3y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2\\left( 2-3y \\right)-3y=1 \\\\ & x=2-3y \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & -9y=-3 \\\\ & x=2-3y \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{aligned} & y=\\dfrac{1}{3} \\\\ & x=2-3.\\dfrac{1}{3} \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=\\dfrac{1}{3} \\\\ & x=1 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $\\left( 1;\\dfrac{1}{3} \\right)$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":353},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"C\u1eb7p s\u1ed1 n\u00e0o l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align} & -4x-4y=4 \\\\ & x+2y=-7 \\\\ \\end{align} \\right.$ ","select":["A. $(5;6)$","B. $(-5;6)$","C. $(5;-6)$ ","D. $(-5;-6)$ "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3<br\/> $\\left\\{ \\begin{aligned} & -4x-4y=4 \\\\ & x+2y=-7 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x+y=-1 \\\\ & x+2y=-7 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x+y=-1 \\\\ & y=-6 \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x-6=-1 \\\\ & y=-6 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=5 \\\\ & y=-6 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m l\u00e0 $(5;-6)$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":354},{"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 $\\left\\{ \\begin{aligned} & 3x-2y=4 \\\\ & -2x+3y=-1 \\\\ \\end{aligned} \\right.$<br\/>Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang? ","select":["A. H\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(1;2)$","B. H\u1ec7 v\u00f4 nghi\u1ec7m","C. H\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(2;1)$","D. H\u1ec7 v\u00f4 s\u1ed1 nghi\u1ec7m "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\left\\{ \\begin{aligned} & 3x-2y=4 \\\\ & -2x+3y=-1 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 6x-4y=8 \\\\ & -6x+9y=-3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 6x-4y=8 \\\\ & 5y=5 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & 6x-4y=8 \\\\ & y=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 6x-4=8 \\\\ & y=1 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=2 \\\\ & y=1 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $\\left( 2;1 \\right)$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":355},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-4"],["3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"X\u00e1c \u0111\u1ecbnh $a, b$ bi\u1ebft h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 2x+by=-4 \\\\ & bx-ay=-5 \\\\ \\end{align} \\right.$ c\u00f3 nghi\u1ec7m l\u00e0 $(1;-2)$ <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $a=$_input_; $b=$_input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>Thay $x=1$ v\u00e0 $y=-2$ v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm $a,b.$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m l\u00e0 $(1;-2)$ n\u00ean ta thay $x=1$ v\u00e0 $y=-2$ v\u00e0o h\u1ec7, ta \u0111\u01b0\u1ee3c:<br\/>$\\left\\{ \\begin{align} & 2-2b=-4 \\\\ & b+2a=-5 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{aligned} & 2b=6 \\\\ & b+2a=-5 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & b=3 \\\\ & b+2a=-5 \\\\ \\end{aligned} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & b=3 \\\\ & 2a=-8 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & b=3 \\\\ & a=-4 \\\\ \\end{aligned} \\right.$<br\/> V\u1eady $a=-4$ v\u00e0 $b=3$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $-4$ v\u00e0 $3$<\/span><\/span>"}]}],"id_ques":356},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $a =-\\dfrac{1}{2}; b = \\dfrac{1}{2}$","B. $a =-\\dfrac{1}{3}; b = \\dfrac{1}{2}$","C. $a =-\\dfrac{1}{3}; b = \\dfrac{1}{3}$"],"ques":"X\u00e1c \u0111\u1ecbnh $a$ v\u00e0 $b$ \u0111\u1ec3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y=ax+b$ \u0111i qua $A\\left( 3;-1 \\right)$ v\u00e0 $B\\left( -3;2 \\right)$ <br\/>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>Thay t\u1ecda \u0111\u1ed9 c\u1ee7a $A$ v\u00e0 $B$ v\u00e0o h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm $a,b.$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 $y=ax+b$ \u0111i qua $A\\left( 3;-1 \\right)$ v\u00e0 $B\\left( -3;2 \\right)$ n\u00ean ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/span><br\/> $ \\left\\{ \\begin{align} & -1=3a+b\\,\\,\\,\\,\\,\\left( 1 \\right) \\\\ & 2=-3a+b\\,\\,\\,\\,\\left( 2 \\right) \\\\ \\end{align} \\right.$ <br\/><span class='basic_left'>C\u1ed9ng t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi nhau, ta \u0111\u01b0\u1ee3c:<br\/> $2b=1\\Leftrightarrow b=\\dfrac{1}{2}$<br\/> Thay $b=\\dfrac{1}{2}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta c\u00f3:<br\/> $-1=3a+\\dfrac{1}{2}\\Leftrightarrow 3a=\\dfrac{-3}{2}\\Leftrightarrow a=-\\dfrac{1}{2}$<br\/> V\u1eady $a=-\\dfrac{1}{2};b=\\dfrac{1}{2}$ <br\/><\/span>"}]}],"id_ques":357},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho \u0111\u01b0\u1eddng th\u1eb3ng $(d)$ c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $\\left( a-1 \\right)x+2y=a$ . X\u00e1c \u0111\u1ecbnh $a$ \u0111\u1ec3 $(d)$ song song v\u1edbi tr\u1ee5c ho\u00e0nh.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b> $a=$_input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>Ph\u01b0\u01a1ng tr\u00ecnh $ax+by=c$ c\u00f3 t\u1eadp nghi\u1ec7m bi\u1ec3u di\u1ec5n b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng $ax+by=c$ $(d).$ <br\/> Khi \u0111\u00f3 $(d)$ song song v\u1edbi tr\u1ee5c ho\u00e0nh n\u1ebfu $a =0$, $b$ v\u00e0 $c$ kh\u00e1c $0$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>\u0110\u01b0\u1eddng th\u1eb3ng $(d)$ song song v\u1edbi tr\u1ee5c ho\u00e0nh khi v\u00e0 ch\u1ec9 khi <br\/>$\\left\\{ \\begin{align} & a-1=0 \\\\ & 2\\ne 0 \\\\ & a\\ne 0 \\\\ \\end{align} \\right.\\Leftrightarrow a=1$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $1.$<\/span><\/span>"}]}],"id_ques":358},{"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"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $m$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 2x-y=0 \\\\ & mx+y=2 \\\\ \\end{align} \\right.$ c\u00f3 nghi\u1ec7m duy nh\u1ea5t.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>$m \\ne $ _input_","hint":"","explain":"<span class='basic_left'>+ X\u00e9t $m=0,$ ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 2x-y=0 \\\\ & y=2 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=1 \\\\ & y=2 \\\\ \\end{align} \\right.$<br\/> Suy ra h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(1;2)$<br\/>+ X\u00e9t $m \\ne 0,$ ta c\u00f3 h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi hai \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 c\u1eaft nhau<br\/> $\\Leftrightarrow \\dfrac{2}{m}\\ne \\dfrac{-1}{1}\\Leftrightarrow m\\ne -2$ <br\/>V\u1eady $m\\ne -2$ th\u00ec h\u1ec7 \u0111\u00e3 cho c\u00f3 nghi\u1ec7m duy nh\u1ea5t.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $-2$.<\/span><\/span>. "}]}],"id_ques":359},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho \u0111\u01b0\u1eddng th\u1eb3ng $(d)$ c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $\\left( a-1 \\right)x+2y=a$ (1). X\u00e1c \u0111\u1ecbnh $a$ \u0111\u1ec3 $(d)$ song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng $x-y=1.$ <br\/><b>\u0110\u00e1p s\u1ed1:<\/b> $a=$_input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>X\u00e9t hai tr\u01b0\u1eddng h\u1ee3p $a-1=0$ v\u00e0 $a-1 \\ne 0$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>+ X\u00e9t $a-1=0 \\Leftrightarrow a=1$ th\u00ec $(1)\\Leftrightarrow 2y=1$<br\/>Ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>$\\left\\{ \\begin{aligned} & 2y=1 \\\\ & x-y=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=\\dfrac{1}{2} \\\\ & x=\\dfrac{3}{2} \\\\ \\end{aligned} \\right.$ <br\/>Suy ra $(d)$ c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng $x - y = 1$ t\u1ea1i \u0111i\u1ec3m $\\left(\\dfrac{3}{2};\\dfrac{1}{2}\\right)$<br\/>+ X\u00e9t $a-1 \\ne 0 \\Leftrightarrow a\\ne 1$<br\/>\u0110\u1ec3 $(d)$ song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng $x-y=1$ th\u00ec<br\/> $\\dfrac{a-1}{1}=\\dfrac{2}{-1}\\ne \\dfrac{a}{1}\\Leftrightarrow \\left\\{ \\begin{align} & a-1=-2 \\\\ & a\\ne -2 \\\\ \\end{align} \\right.\\Leftrightarrow a=-1$<br\/>V\u1eady $a=-1$ th\u00ec th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i.<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $-1.$<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/>Hai \u0111\u01b0\u1eddng th\u1eb3ng $ax+by=c$ v\u00e0 $a'x+b'y=c' $ v\u1edbi $a,b,c,a',b',c' \\ne 0$ song song v\u1edbi nhau khi v\u00e0 ch\u1ec9 khi $\\dfrac{a}{a'}=\\dfrac{b}{b'}\\ne\\dfrac{c}{c'}$.<br\/>Trong b\u00e0i to\u00e1n tr\u00ean, h\u1ecdc sinh th\u01b0\u1eddng kh\u00f4ng \u0111\u1ec3 \u00fd \u0111\u1ebfn $a,b,c,a',b',c' \\ne 0$ n\u00ean khi tr\u00ecnh b\u00e0y t\u1ef1 lu\u1eadn, c\u00e1c em th\u01b0\u1eddng b\u1ecf qua tr\u01b0\u1eddng h\u1ee3p $a-1=0.$ <\/span>"}]}],"id_ques":360},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & ax+ay=3 \\\\ & x-y=3 \\\\ \\end{align} \\right.$ v\u00f4 s\u1ed1 nghi\u1ec7m v\u1edbi m\u1ecdi $a=-1$, \u0111\u00fang hay sai?","select":["A. \u0110\u00fang","B. Sai"],"hint":"","explain":"<span class='basic_left'>V\u1edbi $a=-1,$ ta c\u00f3: $\\left\\{ \\begin{aligned} & -x-y=3 \\\\ & x-y=3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2x=0 \\\\ & x-y=3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=0 \\\\ & y=-3 \\\\ \\end{aligned} \\right.$<br\/> Suy ra h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(0;-3)$<br\/>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 sai<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":361},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["30"],["120"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'>M\u1ed9t s\u00e2n tr\u01b0\u1eddng h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi $300$ $m$ bi\u1ebft chi\u1ec1u d\u00e0i h\u01a1n chi\u1ec1u r\u1ed9ng l\u00e0 $90$ $m.$ T\u00ednh chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng s\u00e2n tr\u01b0\u1eddng.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b><br\/>Chi\u1ec1u r\u1ed9ng s\u00e2n tr\u01b0\u1eddng l\u00e0 _input_ $m$<br\/>Chi\u1ec1u d\u00e0i s\u00e2n tr\u01b0\u1eddng l\u00e0 _input_$m$<\/span>","hint":"Chu vi h\u00ecnh ch\u1eef nh\u1eadt b\u1eb1ng 2 l\u1ea7n t\u1ed5ng chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng.<br\/>","explain":" <span class='basic_left'>G\u1ecdi chi\u1ec1u d\u00e0i s\u00e2n tr\u01b0\u1eddng l\u00e0 $x (m)$ ; chi\u1ec1u r\u1ed9ng l\u00e0 $y (m).$ \u0110i\u1ec1u ki\u1ec7n: $x>y>0$<br\/>V\u00ec chu vi s\u00e2n tr\u01b0\u1eddng l\u00e0 $300$ $m$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $2(x+y)=300$ hay $x+y=150$ (1)<br\/>V\u00ec chi\u1ec1u d\u00e0i h\u01a1n chi\u1ec1u r\u1ed9ng l\u00e0 $90$ $m$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $x \u2013 y= 90$ (2) <br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x+y=150 \\\\ & x-y=90 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & 2y=60 \\\\ & x-y=90 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=30 \\\\ & x=y+90 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=30 \\\\ & x=30+90 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=30 \\\\ & x=120 \\\\ \\end{aligned} \\right.$ <br\/>V\u1eady chi\u1ec1u r\u1ed9ng s\u00e2n tr\u01b0\u1eddng l\u00e0 $30$ $m$ v\u00e0 chi\u1ec1u d\u00e0i l\u00e0 $120$ $m.$ <br\/><span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $30$ v\u00e0 $120$<\/span><\/span>"}]}],"id_ques":362},{"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":"B\u00e1c Nam mang v\u1ecbt v\u00e0 l\u1ee3n ra ch\u1ee3 b\u00e1n. Bi\u1ebft c\u00f3 t\u1ea5t c\u1ea3 $36$ con c\u1ea3 v\u1ecbt v\u00e0 l\u1ee3n. B\u00e1c Nam \u0111\u1ebfm \u0111\u01b0\u1ee3c c\u00f3 $100$ c\u00e1i ch\u00e2n. H\u1ecfi c\u00f3 bao nhi\u00eau con v\u1ecbt v\u00e0 con l\u1ee3n?","select":["A. C\u00f3 $22$ con v\u1ecbt v\u00e0 $14$ con l\u1ee3n ","B. C\u00f3 $14$ con v\u1ecbt v\u00e0 $22$ con l\u1ee3n","C. C\u00f3 $20$ con v\u1ecbt v\u00e0 $16$ con l\u1ee3n","D. C\u00f3 $16$ con v\u1ecbt v\u00e0 $22$ con l\u1ee3n"],"hint":"Gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi \u1ea9n l\u00e0 s\u1ed1 v\u1ecbt v\u00e0 s\u1ed1 con l\u1ee3n.","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 v\u1ecbt l\u00e0 $x$ con, s\u1ed1 l\u1ee3n l\u00e0 $y$ con. \u0110i\u1ec1u ki\u1ec7n: $x,y$ nguy\u00ean d\u01b0\u01a1ng <br\/> V\u00ec t\u1ed5ng s\u1ed1 v\u1ecbt v\u00e0 l\u1ee3n l\u00e0 $36$ con n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=36$ (1)<br\/> V\u00ec v\u1ecbt c\u00f3 $2$ ch\u00e2n n\u00ean t\u1ed5ng s\u1ed1 ch\u00e2n v\u1ecbt l\u00e0 $2x$ ch\u00e2n <br\/> V\u00ec l\u1ee3n c\u00f3 $4$ ch\u00e2n n\u00ean t\u1ed5ng s\u1ed1 ch\u00e2n l\u1ee3n l\u00e0 $4y$ ch\u00e2n <br\/> Do t\u1ed5ng s\u1ed1 ch\u00e2n v\u1ecbt v\u00e0 l\u1ee3n l\u00e0 $100$ ch\u00e2n n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $2x+4y=100$ hay $x+2y=50$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=36 \\\\ & x+2y=50 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& y=14 \\\\ & x=36-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=14 \\\\ & x=36-14 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=22 \\\\ & y=14 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>Suy ra c\u00f3 $22$ con v\u1ecbt v\u00e0 $14$ con l\u1ee3n. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":363},{"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'>V\u00e9 v\u00e0o xem m\u1ed9t bu\u1ed5i h\u00f2a nh\u1ea1c g\u1ed3m lo\u1ea1i $3$ \u0111\u00f4 la v\u00e0 $5$ \u0111\u00f4 la. C\u00f3 $50$ v\u00e9 \u0111\u01b0\u1ee3c b\u00e1n ra v\u00e0 thu v\u1ec1 \u0111\u01b0\u1ee3c $230$ \u0111\u00f4 la. S\u1ed1 v\u00e9 $3$ \u0111\u00f4 la \u0111\u01b0\u1ee3c b\u00e1n ra l\u00e0<\/span>","select":["A. $20$ v\u00e9 ","B. $30$ v\u00e9 ","C. $10$ v\u00e9 "],"hint":"","explain":"<span class='basic_left'>G\u1ecdi $x$ l\u00e0 s\u1ed1 v\u00e9 $3$ \u0111\u00f4 la v\u00e0 $y$ l\u00e0 s\u1ed1 v\u00e9 $5$ \u0111\u00f4 la v\u1edbi $x,y$ nguy\u00ean d\u01b0\u01a1ng <br\/>V\u00ec c\u00f3 $50$ v\u00e9 \u0111\u01b0\u1ee3c b\u00e1n ra n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $x+y=50$ (1)<br\/>T\u1ed5ng thu v\u1ec1 \u0111\u01b0\u1ee3c $230$ \u0111\u00f4 la n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $3x+5y=230$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align} & x+y=50 \\\\ & 3x+5y=230 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & 3x+3y=150 \\\\ & 3x+5y=230 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & 2y=80 \\\\ & 3x+5y=230 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & y=40 \\\\ & 3x+5.40=230 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & y=40 \\\\ & x=10 \\\\ \\end{align} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady c\u00f3 $10$ v\u00e9 lo\u1ea1i $3 $ \u0111\u00f4 la v\u00e0 40 v\u00e9 lo\u1ea1i $5$ \u0111\u00f4 la <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":3}]}],"id_ques":364},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>Qu\u00e3ng \u0111\u01b0\u1eddng $AB$ d\u00e0i $120$ $km.$ Hai \u00f4 t\u00f4 kh\u1edfi h\u00e0nh c\u00f9ng m\u1ed9t l\u00fac t\u1eeb $A$ \u0111\u1ebfn $B.$ \u00d4 t\u00f4 th\u1ee9 nh\u1ea5t ch\u1ea1y nhanh h\u01a1n \u00f4 t\u00f4 th\u1ee9 2 l\u00e0 $10$ $km\/h$ n\u00ean \u0111\u1ebfn tr\u01b0\u1edbc \u00f4 t\u00f4 th\u1ee9 2 l\u00e0 $24$ ph\u00fat. N\u1ebfu g\u1ecdi $x$ l\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t, $y$ l\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 th\u1ee9 hai th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp \u0111\u01b0\u1ee3c l\u00e0: <\/span>","select":["A. $\\left\\{ \\begin{align} & y-x=10 \\\\ & \\dfrac{120}{x}+\\dfrac{2}{5}=\\dfrac{120}{y} \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & x-y=10 \\\\ & \\dfrac{120}{x}+\\dfrac{2}{5}=\\dfrac{120}{y} \\\\ \\end{align} \\right.$ ","C. $\\left\\{ \\begin{align} & x-y=10 \\\\ & \\dfrac{120}{y}+\\dfrac{2}{5}=\\dfrac{120}{x} \\\\ \\end{align} \\right.$ "],"hint":"S\u1eed d\u1ee5ng $t=\\dfrac{s}{v}$ trong \u0111\u00f3 $s$ l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng, $v$ l\u00e0 v\u1eadn t\u1ed1c v\u00e0 $t$ l\u00e0 th\u1eddi gian.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>+ G\u1ecdi \u1ea9n l\u00e0 v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t v\u00e0 \u00f4 t\u00f4 th\u1ee9 hai.<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb gi\u1ea3 thi\u1ebft \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t ch\u1ea1y nhanh h\u01a1n \u00f4 t\u00f4 th\u1ee9 2 l\u00e0 $10$ $km\/h$ <br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1eddi gian c\u1ee7a hai xe t\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>\u0110\u1ed5i $24$ ph\u00fat = $\\dfrac{2}{5}$ gi\u1edd<br\/>G\u1ecdi $x$ l\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t, $y$ l\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 th\u1ee9 hai.<br\/> \u0110i\u1ec1u ki\u1ec7n $x,y>0$<br\/>V\u00ec \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t ch\u1ea1y nhanh h\u01a1n \u00f4 t\u00f4 th\u1ee9 2 l\u00e0 $10$ $km\/h$ n\u00ean ta c\u00f3 $x-y=10$ (1)<br\/>Th\u1eddi gian \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t \u0111i l\u00e0 $\\dfrac{120}{x}$gi\u1edd ; th\u1eddi gian \u00f4 t\u00f4 th\u1ee9 hai \u0111i l\u00e0 $\\dfrac{120}{y}$ gi\u1edd<br\/>V\u00ec \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t \u0111\u1ebfn tr\u01b0\u1edbc \u00f4 t\u00f4 th\u1ee9 hai $\\dfrac{2}{5}$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\dfrac{120}{y}-\\dfrac{120}{x}=\\dfrac{2}{5}$ hay $\\dfrac{120}{x}+\\dfrac{2}{5}=\\dfrac{120}{y}$(2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/span><br\/> $\\left\\{ \\begin{align} & x-y=10 \\\\ & \\dfrac{120}{x}+\\dfrac{2}{5}=\\dfrac{120}{y} \\\\ \\end{align} \\right.$ <span class='basic_left'><br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span>Tr\u01b0\u1edbc khi gi\u1ea3i b\u00e0i to\u00e1n v\u1ec1 chuy\u1ec3n \u0111\u1ed9ng, ta c\u1ea7n \u0111\u01b0a th\u1eddi gian v\u1ec1 c\u00f9ng \u0111\u01a1n v\u1ecb.<\/span>","column":3}]}],"id_ques":365},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"],["1002"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean bi\u1ebft r\u1eb1ng t\u1ed5ng c\u1ee7a ch\u00fang b\u1eb1ng $1012.$ Hai l\u1ea7n s\u1ed1 l\u1edbn c\u1ed9ng s\u1ed1 nh\u1ecf b\u1eb1ng $2014.$<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> S\u1ed1 b\u00e9 l\u00e0 _input_ ; s\u1ed1 l\u1edbn l\u00e0 _input_ <\/span>","hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 nh\u1ecf l\u00e0 $x$ v\u00e0 s\u1ed1 l\u1edbn l\u00e0 $y.$ \u0110i\u1ec1u ki\u1ec7n: $ x < y $ v\u00e0 $ x, y \\in \\mathbb{N}$<br\/>V\u00ec t\u1ed5ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $1012$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=1012$ (1)<br\/>Hai l\u1ea7n s\u1ed1 l\u1edbn l\u00e0 $2y.$ V\u00ec hai l\u1ea7n s\u1ed1 l\u1edbn c\u1ed9ng s\u1ed1 nh\u1ecf b\u1eb1ng $2014$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $x+2y=2014$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x+y=1012 \\\\ & x+2y=2014 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & y=1002 \\\\ & x+y=1012 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=1002 \\\\ & x=10 \\\\ \\end{align} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady s\u1ed1 b\u00e9 l\u00e0 $10$ v\u00e0 s\u1ed1 l\u1edbn l\u00e0 $1002$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $10;1002$<\/span><\/span>"}]}],"id_ques":366},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $x =2,6 ; y = 5$","B. $x =3 ; y = 4$","C. $x = 4 ; y = 5$"],"ques":"<span class='basic_left'>T\u1ea5t c\u1ea3 c\u00f3 $15$ h\u1ed9p g\u1ea1ch l\u00e1t n\u1ec1n v\u00e0 $5$ h\u1ed9p s\u01a1n n\u1eb7ng $64$ $kg.$ H\u1ecfi m\u1ed7i h\u1ed9p g\u1ea1ch v\u00e0 m\u1ed7i h\u1ed9p s\u01a1n n\u1eb7ng bao nhi\u00eau kilogam? Bi\u1ebft $5$ h\u1ed9p g\u1ea1ch n\u1eb7ng h\u01a1n hai h\u1ed9p s\u01a1n l\u00e0 $3$ $kg.$<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>Kh\u1ed1i l\u01b0\u1ee3ng m\u1ed7i h\u1ed9p g\u1ea1ch $x = ? (kg)$, kh\u1ed1i l\u01b0\u1ee3ng m\u1ed7i h\u1ed9p s\u01a1n $y = ? (kg)$<\/span>","hint":"","explain":"<span class='basic_left'>Gi\u1ea3 s\u1eed m\u1ed7i h\u1ed9p g\u1ea1ch n\u1eb7ng $x$ kg, m\u1ed7i h\u1ed9p s\u01a1n n\u1eb7ng $y$ kg, \u0111i\u1ec1u ki\u1ec7n $x>0; y>0$<br\/>V\u00ec $15$ h\u1ed9p g\u1ea1ch v\u00e0 $5$ h\u1ed9p s\u01a1n n\u1eb7ng $64$ kg n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $15x + 5y =64$ (1)<br\/>Do $5$ h\u1ed9p g\u1ea1ch n\u1eb7ng h\u01a1n $2$ h\u1ed9p s\u01a1n $3$ kg n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $5x -2y = 3$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align} & 15x+5y=64 \\\\ & 5x-2y=3 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & 15x+5y=64 \\\\ & 15x-6y=9 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 11y=55 \\\\ & 15x-6y=9 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=5 \\\\ & 15x-6y=9 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & y=5 \\\\ & 15x=39 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & y=5 \\\\ & x=2,6 \\\\ \\end{align} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady m\u1ed7i h\u1ed9p g\u1ea1ch n\u1eb7ng $2,6$ $kg$ v\u00e0 m\u1ed7i h\u1ed9p s\u01a1n n\u1eb7ng $5$ $kg.$<br\/>"}]}],"id_ques":367},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'>Hai \u0111\u1ed9i c\u00f4ng nh\u00e2n c\u00f9ng l\u00e0m m\u1ed9t \u0111o\u1ea1n \u0111\u01b0\u1eddng trong $24$ ng\u00e0y th\u00ec xong. M\u1ed7i ng\u00e0y, ph\u1ea7n vi\u1ec7c \u0111\u1ed9i A l\u00e0m \u0111\u01b0\u1ee3c nhi\u1ec1u g\u1ea5p r\u01b0\u1ee1i \u0111\u1ed9i B. H\u1ecfi n\u1ebfu l\u00e0m m\u1ed9t m\u00ecnh th\u00ec m\u1ed7i \u0111\u1ed9i l\u00e0m xong \u0111o\u1ea1n \u0111\u01b0\u1eddng \u0111\u00f3 trong bao l\u00e2u?<\/span>","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[6],[1],[5],[4],[3]]],"list":[{"point":5,"image":"img\/1.png","left":["<span class='basic_left'>Hai \u0111\u1ed9i l\u00e0m chung trong $24$ ng\u00e0y th\u00ec xong \u0111o\u1ea1n \u0111\u01b0\u1eddng n\u00ean m\u1ed7i ng\u00e0y hai \u0111\u1ed9i l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{24}$ (\u0111o\u1ea1n \u0111\u01b0\u1eddng). Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{24}$(1)<\/span>","V\u1eady \u0111\u1ed9i th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh trong $40$ ng\u00e0y xong \u0111o\u1ea1n \u0111\u01b0\u1eddng, \u0111\u1ed9i th\u1ee9 hai l\u00e0m m\u1ed9t m\u00ecnh trong $60$ ng\u00e0y xong \u0111o\u1ea1n \u0111\u01b0\u1eddng.","G\u1ecdi $x$ l\u00e0 s\u1ed1 ng\u00e0y \u0111\u1ed9i A l\u00e0m m\u1ed9t m\u00ecnh xong \u0111o\u1ea1n \u0111\u01b0\u1eddng; $y$ l\u00e0 s\u1ed1 ng\u00e0y \u0111\u1ed9i B l\u00e0m m\u1ed9t m\u00ecnh xong \u0111o\u1ea1n \u0111\u01b0\u1eddng $(x, y>0).$<br\/> M\u1ed9t ng\u00e0y, \u0111\u1ed9i A l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$(\u0111o\u1ea1n \u0111\u01b0\u1eddng), \u0111\u1ed9i B l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$(\u0111o\u1ea1n \u0111\u01b0\u1eddng). ","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t \u1ea9n ph\u1ee5, ta t\u00ecm \u0111\u01b0\u1ee3c $x=40$ v\u00e0 $y=60$ (tho\u1ea3 m\u00e3n)","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{24} \\\\ & \\dfrac{1}{x}=1,5.\\dfrac{1}{y} \\\\ \\end{align} \\right.$","M\u1ed7i ng\u00e0y, ph\u1ea7n vi\u1ec7c \u0111\u1ed9i A l\u00e0m \u0111\u01b0\u1ee3c nhi\u1ec1u g\u1ea5p r\u01b0\u1ee1i \u0111\u1ed9i B n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $\\dfrac{1}{x}=1,5.\\dfrac{1}{y}$(2) "],"top":120,"hint":"G\u1ecdi $x$ l\u00e0 s\u1ed1 ng\u00e0y \u0111\u1ed9i A l\u00e0m m\u1ed9t m\u00ecnh xong \u0111o\u1ea1n \u0111\u01b0\u1eddng; $y$ l\u00e0 s\u1ed1 ng\u00e0y \u0111\u1ed9i B l\u00e0m m\u1ed9t m\u00ecnh xong th\u1eeda ru\u1ed9ng. <br\/>Ch\u00fa \u00fd: S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c m\u00e0 m\u1ed7i \u0111\u1ed9i l\u00e0m \u0111\u01b0\u1ee3c trong m\u1ed9t ng\u00e0y v\u00e0 s\u1ed1 ng\u00e0y c\u1ea7n thi\u1ebft \u0111\u1ec3 \u0111\u1ed9i \u0111\u00f3 ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng t\u1ec9 l\u1ec7 ngh\u1ecbch. ","explain":"<span class='basic_left'>G\u1ecdi $x$ l\u00e0 s\u1ed1 ng\u00e0y \u0111\u1ed9i A l\u00e0m m\u1ed9t m\u00ecnh xong \u0111o\u1ea1n \u0111\u01b0\u1eddng; $y$ l\u00e0 s\u1ed1 ng\u00e0y \u0111\u1ed9i B l\u00e0m m\u1ed9t m\u00ecnh xong \u0111o\u1ea1n \u0111\u01b0\u1eddng $(x, y > 0)$<br\/>M\u1ed9t ng\u00e0y, \u0111\u1ed9i A l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$(\u0111o\u1ea1n \u0111\u01b0\u1eddng), \u0111\u1ed9i B l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$(\u0111o\u1ea1n \u0111\u01b0\u1eddng). <br\/>Hai \u0111\u1ed9i l\u00e0m chung trong $24$ ng\u00e0y th\u00ec xong \u0111o\u1ea1n \u0111\u01b0\u1eddng n\u00ean m\u1ed7i ng\u00e0y hai \u0111\u1ed9i l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{1}{24}$ (\u0111o\u1ea1n \u0111\u01b0\u1eddng).<br\/>Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{24}$(1)<br\/>M\u1ed7i ng\u00e0y, ph\u1ea7n vi\u1ec7c \u0111\u1ed9i A l\u00e0m \u0111\u01b0\u1ee3c nhi\u1ec1u g\u1ea5p r\u01b0\u1ee1i \u0111\u1ed9i B n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh$\\dfrac{1}{x}=1,5.\\dfrac{1}{y}$(2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{24} \\\\ & \\dfrac{1}{x}=1,5.\\dfrac{1}{y} \\\\ \\end{align} \\right.$ <br\/>\u0110\u1eb7t $u=\\dfrac{1}{x},v=\\dfrac{1}{y}$ , ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh$\\left\\{ \\begin{align} & u+v=\\dfrac{1}{24} \\\\ & u=\\dfrac{3}{2}v \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & \\dfrac{3}{2}v+v=\\dfrac{1}{24} \\\\ & u=\\dfrac{3}{2}v \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & v=\\dfrac{1}{60} \\\\ & u=\\dfrac{3}{2}v \\\\ \\end{align} \\right.$ $ \\Leftrightarrow \\left\\{ \\begin{align} & v=\\dfrac{1}{60} \\\\ & u=\\dfrac{1}{40} \\\\ \\end{align} \\right.$<br\/>Suy ra $\\left\\{ \\begin{align} & \\dfrac{1}{x}=\\dfrac{1}{40} \\\\ & \\dfrac{1}{y}=\\dfrac{1}{60} \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=40 \\\\ & y=60 \\\\ \\end{align} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady \u0111\u1ed9i th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh trong $40$ ng\u00e0y xong \u0111o\u1ea1n \u0111\u01b0\u1eddng, \u0111\u1ed9i th\u1ee9 hai l\u00e0m m\u1ed9t m\u00ecnh trong $60$ ng\u00e0y xong \u0111o\u1ea1n \u0111\u01b0\u1eddng.<\/span>"}]}],"id_ques":368},{"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 c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau: <br\/> $\\left\\{ \\begin{align} & 2x+3y=13 \\\\ & 3x-y=3 \\\\ \\end{align} \\right.$ (I); $\\left\\{ \\begin{align} & 2x+3y=13 \\\\ & 5x+2y=16 \\\\ \\end{align} \\right.$ (II); $\\left\\{ \\begin{align} & 3x-2y=7 \\\\ & 3x+y=10 \\\\ \\end{align} \\right.$ (III) <br\/> Nh\u1eefng 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)","D. H\u1ec7 (I), (II) v\u00e0 (III)"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>C\u00e1ch ch\u1ee9ng minh hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng:<br\/>+ C\u00e1ch 1: Bi\u1ebfn \u0111\u1ed5i t\u01b0\u01a1ng \u0111\u01b0\u01a1ng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y th\u00e0nh h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh kia<br\/>+ C\u00e1ch 2: Ch\u1ec9 ra hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 chung t\u1eadp nghi\u1ec7m<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>X\u00e9t h\u1ec7 (I): C\u1ed9ng t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 (I), ta \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh: $5x+2y=16$<br\/>Thay ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y cho ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7, ta \u0111\u01b0\u1ee3c h\u1ec7 m\u1edbi: <br\/>$\\left\\{ \\begin{align} & 2x+3y=13 \\\\ & 5x+2y=16 \\\\ \\end{align} \\right.$ <br\/> Do \u0111\u00f3 h\u1ec7 (I) v\u00e0 h\u1ec7 (II) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau.<br\/>T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a (I), r\u00fat $y=3x-3$, thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & 2x+3(3x-3)=13 \\\\ & y=3x-3 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 11x=22 \\\\ & y=3x-3 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=2 \\\\ & y=3 \\\\ \\end{align} \\right.$ <br\/> Suy ra $(2;3)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) v\u00e0 c\u0169ng l\u00e0 nghi\u1ec7m c\u1ee7a (II) <br\/> T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a (III), r\u00fat $y=10-3x$, thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ta c\u00f3:<br\/> $\\left\\{ \\begin{align} & 3x-2(10-3x)=7\\\\ & y=10-3x \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 9x=27 \\\\ & y=10-3x \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & x=3 \\\\ & y=1 \\\\ \\end{align} \\right.$<br\/> Suy ra $(3;1)$ l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (III) <br\/> Suy ra h\u1ec7 (III) kh\u00f4ng t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi h\u1ec7 (I) v\u00e0 (II) <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span><\/span>","column":2}]}],"id_ques":369},{"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'><br\/> <span class='basic_green'> H\u01b0\u1edbng d\u1eabn <\/span> <br\/>X\u00e9t hai tr\u01b0\u1eddng h\u1ee3p $m=0$ v\u00e0 $m \\ne 0$.<br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m 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 song song <br\/> <span class='basic_green'> B\u00e0i gi\u1ea3i<\/span> <br\/> Tr\u01b0\u1eddng h\u1ee3p 1: $m = 0$, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & y=-3 \\\\ & x=2 \\\\ \\end{align} \\right.$ <br\/> Suy ra v\u1edbi $m = 0$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t (lo\u1ea1i) <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $m \\ne 0$ <br\/> $\\left\\{ \\begin{align} & mx-y=3 \\\\ & x-my=2 \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align} & y=mx - 3\\,\\,(1) \\\\ & y=\\dfrac{1}{m}x - \\dfrac{2}{m}\\,\\,(2) \\\\ \\end{align} \\right.$ <br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m khi v\u00e0 ch\u1ec9 khi c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng (1) v\u00e0 (2) song song <br\/> $\\Leftrightarrow \\left\\{ \\begin{align} & m=\\dfrac{1}{m} \\\\ & -3 \\ne -\\dfrac{2}{m} \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & m^2= 1 \\\\ & 3m\\ne 2 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{align} & m= \\pm 1 \\\\ & m\\ne \\dfrac{2}{3} \\\\ \\end{align} \\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":370}],"lesson":{"save":0,"level":1}}