# How do you solve 4x - y = -5 and -2x + 3y = 10?

Sep 6, 2015

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

#### Explanation:

Your system of equations looks like this

$\left\{\begin{matrix}4 x - y = - 5 \\ - 2 x + 3 y = 10\end{matrix}\right.$

Multiply the second equation by $2$ to get

$\left\{\begin{matrix}4 x - y = - 5 \\ - 4 x + 6 y = 20\end{matrix}\right.$

Notice that if you add the left-hand side of the equations and the right-hand sides of the equations separately, you can eliminate the $x$-term.

This will allow you to find the value of $y$, since you'll be left with one equation with one unknown, $y$.

$\left\{\begin{matrix}4 x - y = - 5 \\ - 4 x + 6 y = 20\end{matrix}\right.$
stackrel("--------------------------------------------")
$\textcolor{red}{\cancel{\textcolor{b l a c k}{4 x}}} - y - \textcolor{red}{\cancel{\textcolor{b l a c k}{4 x}}} + 6 y = - 5 + 20$

$5 y = 15 \implies y = \textcolor{g r e e n}{3}$

Now take the value of $y$ into one of the two original equations to solve for $x$

$4 x - 3 = - 5$

$4 x = - 2 \implies x = \textcolor{g r e e n}{- \frac{1}{2}}$