Giải câu 2 trang 10 sách toán VNEN lớp 9 tập 2

a) $\left\{\begin{matrix}x + 3y = 4\\ 4x - 5y = 18\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 4 - 3y \\ 4(3 - 3y) - 5y = 18\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 4 - 3y \\ 17y = -2\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 4 - 3y \\ y = \frac{-2}{17}\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x =  \frac{74}{17}\\ y = \frac{-2}{17}\end{matrix}\right.$

b) $\left\{\begin{matrix}5x - 3y = 5\\ 2x + 5y = 33\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{3y}{5} + 1\\ 2(\frac{3y}{5} + 1) + 5y = 33\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{3y}{5} + 1\\ \frac{31y}{5} = 31\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{3y}{5} + 1\\ y = 5\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 4\\ y = 5\end{matrix}\right.$

c) $\left\{\begin{matrix}\frac{x}{2} - \frac{y}{3} = 0\\ 5x + y = 13\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{2y}{3}\\ 5\times \frac{2y}{3} + y = 13\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{2y}{3}\\ \frac{13y}{3} = 13\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 2\\ y = 3\end{matrix}\right.$

d) $\left\{\begin{matrix}x + 2y = \frac{7}{6}\\ 4x + 6y = 4\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{7}{6} - 2y\\ 4(\frac{7}{6} - 2y) + 6y = 4\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{7}{6} - 2y\\ 2y = \frac{2}{3}\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{1}{2}\\ y = \frac{1}{3}\end{matrix}\right.$