Toán Lớp 9: giải hệ phg trình bằng phương pháp đặt ẩn phụ:
2/x+2y +1/y+2x =3
4/x+2y -3/y+2x =1
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Toán Lớp 9: giải hệ phg trình bằng phương pháp đặt ẩn phụ:
2/x+2y +1/y+2x =3
4/x+2y -3/y+2x =1
Comments ( 1 )
Giải đáp: $\left( {x;y} \right) = \left( {\dfrac{1}{3};\dfrac{1}{3}} \right)$
Lời giải và giải thích chi tiết:
$\begin{array}{l}
Dkxd:\left\{ \begin{array}{l}
x + 2y \ne 0\\
y + 2x \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne – 2y\\
y \ne – 2x
\end{array} \right.\\
Dat:\dfrac{1}{{x + 2y}} = a;\dfrac{1}{{y + 2x}} = b\\
\left\{ \begin{array}{l}
\dfrac{2}{{x + 2y}} + \dfrac{1}{{y + 2x}} = 3\\
\dfrac{4}{{x + 2y}} – \dfrac{3}{{y + 2x}} = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2a + b = 3\\
4a – 3b = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
4a + 2b = 6\\
4a – 3b = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
5b = 5\\
2a + b = 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
b = 1\\
2a = 3 – b = 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
b = 1\\
a = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{1}{{x + 2y}} = 1\\
\dfrac{1}{{y + 2x}} = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x + 2y = 1\\
y + 2x = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x + 2y = 1\\
2x + y = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2x + 4y = 2\\
2x + y = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
3y = 1\\
x + 2y = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
y = \dfrac{1}{3}\\
x = 1 – 2y = 1 – 2.\dfrac{1}{3} = \dfrac{1}{3}
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left( {\dfrac{1}{3};\dfrac{1}{3}} \right)
\end{array}$