# How do you solve this system of equations: 2x + y = - 2 and 5x + 3y = - 8?

Aug 2, 2018

x = 2
y = -6

#### Explanation:

The question is asking to solve for 2 unknowns using 2 equations.

Let's start by rearranging one of the equation. That will make it easier to substitute. You can start with either equation, but I find the first equation easier to rearrange:
$2 x + y = - 2$
$2 x + y \textcolor{red}{- 2 x} = - 2 \textcolor{red}{- 2 x}$ [move 2x to the other side]
$y = - 2 - 2 x$ [simplify]

and insert that into the second equation:
$5 x + 3 y = - 8$
$5 x + 3 \left(\textcolor{red}{- 2 - 2 x}\right) = - 8$ [substitute "-2-2x" for y]
$5 x + \textcolor{red}{- 6 - 6 x} = - 8$ [multiply out]
$- 6 - x = - 8$ [simplify]
$x = 2$

Now that we have found the value for x, we can substitute in the value for x in any one of the equation to find the value for y.
$y = - 2 - 2 x$
$y = - 2 - 2 \left(2\right)$ [substitute in the value of x]
$y = - 6$