# How do you solve the following system using substitution?: x-3y=2, x+y=-10

Oct 21, 2015

#### Answer:

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

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} x - 3 y = 2$
[2]$\textcolor{w h i t e}{\text{XXX}} x + y = - 10$

Rearrange [1], isolating $x$ on one side:
[3]$\textcolor{w h i t e}{\text{XXX}} x = 3 y + 2$

Substitute $\left(3 y + 2\right)$ for $x$ in [2]
[4]$\textcolor{w h i t e}{\text{XXX}} \left(3 y + 2\right) + y = - 10$

Simplify
[5]$\textcolor{w h i t e}{\text{XXX}} 4 y = - 12$

[6]$\textcolor{w h i t e}{\text{XXX}} y = - 3$

Substitute $\left(- 3\right)$ for $y$ in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} x - 3 \left(- 3\right) = 2$

[8]$\textcolor{w h i t e}{\text{XXX}} x + 9 = 2$

[9]$\textcolor{w h i t e}{\text{XXX}} x = - 7$