# How do you solve 4y = 11 - 3x and 3x + 2y = -5?

Jun 18, 2018

The solution is $\left\{\begin{matrix}x = - 7 \\ y = 8\end{matrix}\right.$

#### Explanation:

Solve as follows

$\left\{\begin{matrix}4 y = 11 - 3 x \\ 3 x + 2 y = - 5\end{matrix}\right.$

Rewrite the equations as

$\left\{\begin{matrix}3 x = 11 - 4 y \\ 3 x = - 5 - 2 y\end{matrix}\right.$

Therefore,

$11 - 4 y = - 5 - 2 y$

$\iff$, $4 y - 2 y = 11 + 5$

$\iff$, $2 y = 16$

$\iff$, $y = \frac{16}{2} = 8$

$3 x = 11 - 4 \cdot 8 = 11 - 32 = - 21$

$\iff$, $x = - \frac{21}{3} = - 7$