# How do you solve 2x – y = –2 and x = 14 + 2y?

Aug 11, 2015

$\left\{\begin{matrix}x = - 6 \\ y = - 10\end{matrix}\right.$

#### Explanation:

Your system of equations looks like this

$\left\{\begin{matrix}2 x - y = - 2 \\ x = 14 + 2 y\end{matrix}\right.$

To solve this system by substitution, use the value of $x$ from the second equation to find the value of $y$ in the first equation.

$2 \cdot \left(14 + 2 y\right) - y = - 2$

$28 \cdot 4 y - y = - 2$

$3 y = - 30 \implies y = \frac{- 30}{3} = \textcolor{g r e e n}{- 10}$

Now take this value back to the second equation and find $x$

$x = 14 + 2 \cdot \left(- 10\right)$

$x = 14 - 20 = \textcolor{g r e e n}{- 6}$

The two solutions to your system of equations are

$\left\{\begin{matrix}x = - 6 \\ y = - 10\end{matrix}\right.$