# How do you solve this system of equations: y=2x-3 and y=-3x+2?

Jun 15, 2018

The solution is $\left\{\begin{matrix}y = - 1 \\ x = 1\end{matrix}\right.$

#### Explanation:

The system of equations is

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

$\iff$, $\left\{\begin{matrix}y = 2 x - 3 \\ 2 x - 3 = - 3 x + 2\end{matrix}\right.$

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

$\iff$, $\left\{\begin{matrix}y = 2 x - 3 \\ x = 1\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}y = - 1 \\ x = 1\end{matrix}\right.$