Toán Lớp 7: a) x+y=4(x-y) và x-2y=x/y
b) x-y=4(x-y) và x+y=x/y
Giúp mik vs ạ
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Toán Lớp 7: a) x+y=4(x-y) và x-2y=x/y
b) x-y=4(x-y) và x+y=x/y
Giúp mik vs ạ
Comments ( 1 )
a)x + y = 4\left( {x – y} \right)\\
\Leftrightarrow x + y = 4x – 4y\\
\Leftrightarrow 4x – x = y + 4y\\
\Leftrightarrow 3x = 5y\\
\Leftrightarrow \dfrac{x}{y} = \dfrac{5}{3}\\
Khi:x – 2y = \dfrac{x}{y}\\
\Leftrightarrow x – 2y = \dfrac{5}{3}\\
Khi:\dfrac{x}{y} = \dfrac{5}{3}\\
\Leftrightarrow \dfrac{x}{5} = \dfrac{y}{3} = \dfrac{{2y}}{6} = \dfrac{{x – 2y}}{{5 – 6}} = \dfrac{{\dfrac{5}{3}}}{{ – 1}} = – \dfrac{5}{3}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{ – 5}}{3}.5 = – \dfrac{{25}}{3}\\
y = – \dfrac{5}{3}.3 = – 5
\end{array} \right.\\
Vậy\,x = \dfrac{{ – 25}}{3};y = – 5\\
b)\\
x – y = 4\left( {x – y} \right)\\
\Leftrightarrow 3\left( {x – y} \right) = 0\\
\Leftrightarrow x – y = 0\\
\Leftrightarrow x = y\\
\Leftrightarrow \dfrac{x}{y} = 1\\
Khi:x + y = \dfrac{x}{y}\\
\Leftrightarrow x + y = 1\\
\Leftrightarrow x = y = \dfrac{1}{2}\\
Vậy\,x = y = \dfrac{1}{2}
\end{array}$