Giải câu 2 trang 12 sách toán VNEN lớp 9 tập 2.
a) $\left\{\begin{matrix}x - 2y = -8\\ 7x + 2y = -8\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}8x= -16\\ x - 2y = -8\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x= -2\\ x - 2y = -8\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x= -2\\ y = 3\end{matrix}\right.$
b) $\left\{\begin{matrix}2x - 5y = -1,1\\ 5x - 2y = 0,1\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}20x - 50y = -11\\ 50x - 20y = 1\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}100x - 250y = -55\\ 100x - 40y = 2\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}210y = 57\\ 50x - 20y = 1\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}y = \frac{19}{70}\\ x = \frac{9}{70}\end{matrix}\right.$
c) $\left\{\begin{matrix}\frac{x}{3} + \frac{y}{4} = -\frac{1}{12}\\ -3x + 2y = -12\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}4x + 3y = -1\\ -3x + 2y = -12\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}12x + 9y = -3\\ -12x + 8y = -48\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}17y = -51\\ -3x + 2y = -12\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}y = -3\\ -3x + 2y = -12\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix} x = 2\\ y = -3\end{matrix}\right.$
d) $\left\{\begin{matrix}x + 2y = 5\sqrt{5}\\ \sqrt{5}x + y = 5 + 2\sqrt{5}\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x + 2y = 5\sqrt{5}\\ 2\sqrt{5}x + 2y = 10 + 4\sqrt{5}\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x + 2y = 5\sqrt{5}\\ (2\sqrt{5} - 1)x = -\sqrt{5} + 10\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x = \frac{-\sqrt{5} + 10}{2\sqrt{5} - 1}\\ x + 2y = 5\sqrt{5}\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x = \frac{(-\sqrt{5} + 10)(2\sqrt{5} + 1)}{19}\\ x + 2y = 5\sqrt{5}\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x = \frac{19\sqrt{5}}{19}\\ x + 2y = 5\sqrt{5}\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x = \sqrt{5}\\ y = 2\sqrt{5}\end{matrix}\right.$