# How do you solve the following linear system -4x - 3y = 5 , x - 4y = -3 ?

Apr 30, 2018

The solutions are $S = \left\{\begin{matrix}x = - \frac{29}{19} \\ y = \frac{7}{19}\end{matrix}\right.$

#### Explanation:

The system of equations are

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

$\iff$, $L 2 \leftarrow \left(L 2 + 4 L 1\right)$

$\left\{\begin{matrix}x - 4 y = - 3 \\ 0 - 19 y = - 7\end{matrix}\right.$

$\iff$, $L 2 \leftarrow \left(\frac{L 2}{19}\right)$

$\left\{\begin{matrix}x - 4 y = - 3 \\ y = \frac{7}{19}\end{matrix}\right.$

$\iff$

$\left\{\begin{matrix}x = 4 \cdot \frac{7}{19} - 3 = - \frac{29}{19} \\ y = \frac{7}{19}\end{matrix}\right.$

$\iff$

$\left\{\begin{matrix}x = - \frac{29}{19} \\ y = \frac{7}{19}\end{matrix}\right.$