{"segment":[{"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":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{9} = \\dfrac{y}{5} = \\dfrac{z}{10}$ v\u00e0 $x - y + z = 70$ ","select":["A. $x = 9; y = 5; z = 10 $ ","B. $x = 27; y = 15; z = 30 $ ","C. $x = 36; y = 20; z = 40 $ ","D. $x = 45; y = 25; z = 50 $ "],"hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng,hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ v\u00e0 $x - y + z = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = \\dfrac{x-y+z}{a-b+c} = \\dfrac{M}{a-b+c}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y, z$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{9} = \\dfrac{y}{5} = \\dfrac{z}{10} = \\dfrac{x-y+z}{9-5+10} = \\dfrac{70}{14} = 5 $ <br\/> Suy ra: $\\dfrac{x}{9} = 5 \\Rightarrow x = 9.5 = 45 \\\\ \\dfrac{y}{5} = 5 \\Rightarrow y = 5.5 = 25 \\\\ \\dfrac{z}{10} = 5 \\Rightarrow z = 10.5 = 50$ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u00e0: $\\begin{cases} x = 45 \\\\ y = 25 \\\\ z = 50 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":301},{"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":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{8} = \\dfrac{y}{5} = \\dfrac{z}{12}$ v\u00e0 $x + y + z = -100 $ ","select":["A. $x = 32; y = 20; z = 48 $ ","B. $x = -32; y = -20; z = -48 $ ","C. $x = -32; y = -20; z = 48 $ "],"hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng,hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ v\u00e0 $x + y + z = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = \\dfrac{x+y+z}{a+b+c} = \\dfrac{M}{a+b+c}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y, z$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{8} = \\dfrac{y}{5} = \\dfrac{z}{12} = \\dfrac{x+y+z}{8+5+12} = \\dfrac{-100}{25} = -4 $ <br\/> Suy ra: $\\dfrac{x}{8} = -4 \\Rightarrow x = (-4).8 = -32 \\\\ \\dfrac{y}{5} = -4 \\Rightarrow y = (-4).5 = -20 \\\\ \\dfrac{z}{12} = -4 \\Rightarrow z = (-4).12 = -48 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u00e0: $\\begin{cases} x = -32 \\\\ y = -20 \\\\ z = -48 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":1}]}],"id_ques":302},{"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":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{7} = \\dfrac{y}{10} = \\dfrac{z}{13}$ v\u00e0 $x + y + z = 120$ ","select":["A. $x = 28; y = 40; z = 52 $ ","B. $x = 21; y = 30; z = 36 $ ","C. $x = 35; y = 50; z = 65 $ "],"hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng,hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ v\u00e0 $x + y + z = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = \\dfrac{x+y+z}{a+b+c} = \\dfrac{M}{a+b+c}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y, z$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{7} = \\dfrac{y}{10} = \\dfrac{z}{13} = \\dfrac{x+y+z}{7+10+13} = \\dfrac{120}{30} = 4 $ <br\/> Suy ra: $\\dfrac{x}{7} = 4 \\Rightarrow x = 4.7 = 28 \\\\ \\dfrac{y}{10} = 4 \\Rightarrow y = 4.10 = 40 \\\\ \\dfrac{z}{13} = 4 \\Rightarrow z = 4.13 = 52 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u00e0: $\\begin{cases} x = 28 \\\\ y = 40 \\\\ z = 52 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":1}]}],"id_ques":303},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["14"],["26"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{7} = \\dfrac{y}{13}$ v\u00e0 $x + y = 40$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_; $y = $ _input_","hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{7} = \\dfrac{y}{13} = \\dfrac{x+y}{7+13} = \\dfrac{40}{20} = 2 $ <br\/> Suy ra: $\\dfrac{x}{7} = 2 \\Rightarrow x = 2.7 = 14 \\\\ \\dfrac{y}{13} = 2 \\Rightarrow y = 2.13 = 26$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 14 \\\\ y = 26 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":304},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-6"],["-15"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{2} = \\dfrac{y}{5}$ v\u00e0 $x + y = -21$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_; $y = $ _input_","hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{2} = \\dfrac{y}{5} = \\dfrac{x+y}{2+5} = \\dfrac{-21}{7} = -3 $ <br\/> Suy ra: $\\dfrac{x}{2} = -3 \\Rightarrow x = (-3).2 = -6 \\\\ \\dfrac{y}{5} = -3 \\Rightarrow y = (-3).5 = -15$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = -6 \\\\ y = -15 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":305},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["30"],["60"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{3} = \\dfrac{y}{6}$ v\u00e0 $x + y = 90$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$ y = $ _input_","hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{3} = \\dfrac{y}{6} = \\dfrac{x+y}{3+6} = \\dfrac{90}{9} = 10 $ <br\/> Suy ra: $\\dfrac{x}{3} = 10 \\Rightarrow x = 10.3 = 30 \\\\ \\dfrac{y}{6} = 10 \\Rightarrow y = 10.6 = 60$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 30 \\\\ y = 60 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":306},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-8"],["20"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{-2} = \\dfrac{y}{5}$ v\u00e0 $x + y = 12$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$ y = $ _input_","hint":"\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{-2} = \\dfrac{y}{5} = \\dfrac{x+y}{-2+5} = \\dfrac{12}{3} = 4 $ <br\/> Suy ra: $\\dfrac{x}{-2} = 4 \\Rightarrow x = 4.(-2) = -8 \\\\ \\dfrac{y}{5} = 4 \\Rightarrow y = 4.5 = 20$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = -8 \\\\ y = 20 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":307},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["4"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $2x = 3y$ v\u00e0 $x + y = 10$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_; $y = $ _input_","hint":" \u0110\u01b0a $2x = 3y$ v\u1ec1 t\u1ec9 l\u1ec7 th\u1ee9c r\u1ed3i \u00e1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $ 2x = 3y \\Leftrightarrow \\dfrac{x}{3} = \\dfrac{y}{2}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{3} = \\dfrac{y}{2} = \\dfrac{x+y}{3+2} = \\dfrac{10}{5} = 2 $ <br\/> Suy ra: $\\dfrac{x}{3} = 2 \\Rightarrow x = 2.3 = 6 \\\\ \\dfrac{y}{2} = 2 \\Rightarrow y = 2.2 = 4$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 6 \\\\ y = 4 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":308},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["25"],["15"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $3x = 5y$ v\u00e0 $x + y = 40$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$ y = $ _input_","hint":" \u0110\u01b0a $3x = 5y$ v\u1ec1 t\u1ec9 l\u1ec7 th\u1ee9c r\u1ed3i \u00e1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $ 3x = 5y \\Leftrightarrow \\dfrac{x}{5} = \\dfrac{y}{3}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{5} = \\dfrac{y}{3} = \\dfrac{x+y}{5+3} = \\dfrac{40}{8} = 5 $ <br\/> Suy ra: $\\dfrac{x}{5} = 5 \\Rightarrow x = 5.5 = 25 \\\\ \\dfrac{y}{3} = 5 \\Rightarrow y = 5.3 = 15$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 25 \\\\ y = 15 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":309},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["50"],["-20"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $-2x = 5y$ v\u00e0 $x + y = 30$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$ y = $ _input_","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $ -2x = 5y \\Leftrightarrow \\dfrac{x}{5} = \\dfrac{y}{-2}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{5} = \\dfrac{y}{-2} = \\dfrac{x+y}{5+(-2)} = \\dfrac{30}{3} = 10 $ <br\/> Suy ra: $\\dfrac{x}{5} = 10 \\Rightarrow x = 10.5 = 50 \\\\ \\dfrac{y}{-2} = 10 \\Rightarrow y = 10.(-2) = -20$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 50 \\\\ y = -20 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":310},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-12"],["-28"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{3} = \\dfrac{y}{7}$ v\u00e0 $x - y = 16$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$ y = $ _input_","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x - y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x-y}{a-b} = \\dfrac{M}{a-b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{3} = \\dfrac{y}{7} = \\dfrac{x-y}{3-7} = \\dfrac{16}{-4} = -4 $ <br\/> Suy ra: $\\dfrac{x}{3} = -4 \\Rightarrow x = (-4).3 = -12 \\\\ \\dfrac{y}{7} = -4 \\Rightarrow y = (-4).7 = -28$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = -12 \\\\ y = -28 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":311},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-33"],["-44"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $4x = 3y$ v\u00e0 $x - y = 11$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$y = $ _input_","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x - y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x-y}{a-b} = \\dfrac{M}{a-b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $4x = 3y \\Leftrightarrow \\dfrac{x}{3} = \\dfrac{y}{4} $ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{3} = \\dfrac{y}{4} = \\dfrac{x-y}{3-4} = \\dfrac{11}{-1} = -11 $ <br\/> Suy ra: $\\dfrac{x}{3} = -11 \\Rightarrow x = (-11).3 = -33 \\\\ \\dfrac{y}{4} = -11 \\Rightarrow y = (-11).4 = -44$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = -33 \\\\ y = -44 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":312},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["12"],["-21"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{4} = \\dfrac{y}{-7}$ v\u00e0 $x - y = 33$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$ y = $ _input_","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x - y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x-y}{a-b} = \\dfrac{M}{a-b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{4} = \\dfrac{y}{-7} = \\dfrac{x-y}{4-(-7)} = \\dfrac{33}{11} = 3 $ <br\/> Suy ra: $\\dfrac{x}{4} = 3 \\Rightarrow x = 3.4 = 12 \\\\ \\dfrac{y}{-7} = 3 \\Rightarrow y = 3.(-7) = -21$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 12 \\\\ y = -21 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":313},{"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":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{3} = \\dfrac{y}{5}$ v\u00e0 $x + y = 16$ ","select":["A. $x = 6; y = 10 $ ","B. $x = 9; y = 15 $ ","C. $x = 3; y = 5 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{x+y}{3+5} = \\dfrac{16}{8} = 2 $ <br\/> Suy ra: $\\dfrac{x}{3} = 2 \\Rightarrow x = 2.3 = 6 \\\\ \\dfrac{y}{5} = 2 \\Rightarrow y = 2.5 = 10$ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 6 \\\\ y = 10 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":3}]}],"id_ques":314},{"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":" N\u1ebfu $\\dfrac{x}{5} = \\dfrac{y}{7}$ v\u00e0 $x + y = 24$ th\u00ec: ","select":["A. $x = 5; y = 7 $ ","B. $x = 10; y = 14 $ ","C. $x = -10; y = -14 $ ","D. $x = -9; y = -21 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{5} = \\dfrac{y}{7} = \\dfrac{x+y}{5+7} = \\dfrac{24}{12} = 2 $ <br\/> Suy ra: $\\dfrac{x}{5} = 2 \\Rightarrow x = 2.5 = 10 \\\\ \\dfrac{y}{7} = 2 \\Rightarrow y = 2.7 = 14$ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 10 \\\\ y = 14 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":315},{"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":" N\u1ebfu $\\dfrac{x}{-5} = \\dfrac{y}{7}$ v\u00e0 $x + y = -10$ th\u00ec: ","select":["A. $x = -25; y = 35 $ ","B. $x = 35; y = -25 $ ","C. $x = -35; y = 25 $ ","D. $x = 25; y = -35 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{-5} = \\dfrac{y}{7} = \\dfrac{x+y}{-5+7} = \\dfrac{-10}{2} = -5 $ <br\/> Suy ra: $\\dfrac{x}{-5} = -5 \\Rightarrow x = (-5).(-5) = 25 \\\\ \\dfrac{y}{7} = -5 \\Rightarrow y = (-5).7 = -35$ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 25 \\\\ y = -35 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":316},{"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":" Bi\u1ebft r\u1eb1ng $x : 7 = y : 6$ v\u00e0 $x - y = 15 $. Khi \u0111\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a x v\u00e0 y l\u00e0: ","select":["A. $x = 105; y = 90 $ ","B. $x = 103; y = 86 $ ","C. $x = 110; y = 100 $ ","D. $x = 98; y = 84 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x - y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x-y}{a-b} = \\dfrac{M}{a-b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>T\u1eeb gi\u1ea3 thi\u1ebft ta c\u00f3: $ \\dfrac{x}{7} = \\dfrac{y}{6}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{7} = \\dfrac{y}{6} = \\dfrac{x-y}{7-6} = \\dfrac{15}{1} = 15 $ <br\/> Suy ra: $\\dfrac{x}{7} = 15 \\Rightarrow x = 15.7 = 105 \\\\ \\dfrac{y}{6} = 15 \\Rightarrow y = 16.5 = 90 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 105 \\\\ y = 90 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":317},{"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":" Cho $7a = 4b$ v\u00e0 $a + b = -22. $ Khi \u0111\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a a v\u00e0 b l\u00e0: ","select":["A. $a = -14; b = -8 $ ","B. $a = -8; b = -14 $ ","C. $a = 8; b = 14 $ ","D. $a = -14; b = 8 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u1ed5ng c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x + y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x+y}{a+b} = \\dfrac{M}{a+b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{a}{4} = \\dfrac{b}{7} = \\dfrac{a+b}{4+7} = \\dfrac{-22}{11} = -2$ <br\/> Suy ra: $\\dfrac{a}{4} = -2 \\Rightarrow a = (-2).4 = -8 \\\\ \\dfrac{b}{7} = -2 \\Rightarrow y = (-2).7 = -14 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a$ v\u00e0 $b$ l\u00e0: $\\begin{cases} a = -8 \\\\ b = -14 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":318},{"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":" N\u1ebfu $\\dfrac{a}{11} = \\dfrac{b}{3}$ v\u00e0 $a - b = -24 $ th\u00ec: ","select":["A. $a = -33; b = -9 $ ","B. $a = 9; b = 33 $ ","C. $a = -9; b = -33 $ ","D. $a = 33; b = 9 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x - y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x-y}{a-b} = \\dfrac{M}{a-b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{a}{11} = \\dfrac{b}{3} = \\dfrac{a-b}{11-3} = \\dfrac{-24}{8} = -3$ <br\/> Suy ra: $\\dfrac{a}{11} = -3 \\Rightarrow a = (-3).11 = -33 \\\\ \\dfrac{b}{3} = -3 \\Rightarrow y = (-3).3 = -9 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a$ v\u00e0 $b$ l\u00e0: $\\begin{cases} a = -33 \\\\ b = -9 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":319},{"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":" T\u00ecm hai s\u1ed1 $x$ v\u00e0 $y$ bi\u1ebft: $\\dfrac{x}{2} = \\dfrac{y}{-5}$ v\u00e0 $x - y = -7 ?$ ","select":["A. $x = 2; y = 5 $ ","B. $x = -2; y = 5 $ ","C. $x = -2; y = -5 $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft hi\u1ec7u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3<\/b> <br\/> <i> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b}$ v\u00e0 $x - y = M$ <br\/> Th\u00ec $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{x-y}{a-b} = \\dfrac{M}{a-b}$ <br\/> T\u1eeb \u0111\u00f3 t\u00ecm \u0111\u01b0\u1ee3c $x, y$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{2} = \\dfrac{y}{-5} = \\dfrac{x-y}{2-(-5)} = \\dfrac{-7}{7} = -1 $ <br\/> Suy ra: $\\dfrac{x}{2} = -1 \\Rightarrow x = (-1).2 = -2 \\\\ \\dfrac{y}{-5} = -1 \\Rightarrow y = (-1).(-5) = 5$ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = -2 \\\\ y = 5 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":3}]}],"id_ques":320}],"lesson":{"save":0,"level":1}}