# How do you solve x + y = -7 and 3x + y = -9?

Aug 1, 2015

$x = - 1$; $y = - 6$

#### Explanation:

You could solve this system of equations by using the multiplication method.

To do that, start by multiplying both sides of the first equation by $- 3$.

$- 3 \cdot \left(x + y\right) = - 3 \cdot \left(- 7\right)$

$- 3 x - 3 y = 21$

The system of equations will now be

$\left\{\begin{matrix}- 3 x - 3 y = 21 \\ 3 x + y = - 9\end{matrix}\right.$

Next, add left sides and the right sides of the two equations separately to eliminate the terms that contain $x$

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} - 3 y + \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} + y = 21 - 9$

$- 2 y = 12$

Divide both sides of the equation by $- 2$ to get the value of $y$

$\frac{- \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} y}{- \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} = \frac{12}{- 2} \implies y = \textcolor{g r e e n}{- 6}$

Now that you know the value of $y$, use it in one of the two equations to determine the value of $x$

$3 x + y = - 9$

$3 x + \left(- 6\right) = - 9$

This is equivalent to

$3 x = - 9 + 6 = - 3$

Now divide both sides of this equation by $3$ to get the value of $x$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{- 3}{3} \implies x = \textcolor{g r e e n}{- 1}$

The two solutions are

$\left\{\begin{matrix}x = - 1 \\ y = - 6\end{matrix}\right.$