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

Mar 21, 2018

See a solution process below:

#### Explanation:

Step 1) Solve the first equation for $x$:

$5 x + 5 y = - 10$

$\frac{5 x + 5 y}{\textcolor{red}{5}} = - \frac{10}{\textcolor{red}{5}}$

$\frac{5 x}{\textcolor{red}{5}} + \frac{5 y}{\textcolor{red}{5}} = - 2$

$x + y = - 2$

$x + y - \textcolor{red}{y} = - 2 - \textcolor{red}{y}$

$x + 0 = - 2 - y$

$x = - 2 - y$

Step 2) Substitute $\left(- 2 - y\right)$ for $x$ in the second equation and solve for $y$:

$- 4 x + 2 y = - 10$ becomes:

$- 4 \left(- 2 - y\right) + 2 y = - 10$

$\left(- 4 \times - 2\right) + \left(- 4 \times - y\right) + 2 y = - 10$

$8 + 4 y + 2 y = - 10$

$8 + \left(4 + 2\right) y = - 10$

$8 + 6 y = - 10$

$8 - \textcolor{red}{8} + 6 y = - 10 - \textcolor{red}{8}$

$0 + 6 y = - 18$

$6 y = - 18$

$\frac{6 y}{\textcolor{red}{6}} = - \frac{18}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} y}{\cancel{\textcolor{red}{6}}} = - 3$

$y = - 3$

Step 3) Substitute $- 3$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 2 - y$ becomes:

$x = - 2 - \left(- 3\right)$

$x = - 2 + 3$

$x = 1$

The Solution Is:

$x = 1$ and $y = - 3$

Or

$\left(1 , - 3\right)$