# How do you solve the following system using substitution?: -2x+5y=-2, x-3y=3

Oct 26, 2015

Re-write one of the equations into the form
color(white)("XXX")x= "an expression"
then substitute the "expression" for $x$ in the other equation.
$\textcolor{w h i t e}{\text{XXX}} \left(x , y\right) = \left(- 9 , - 4\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} - 2 x + 5 y = - 2$
[2]$\textcolor{w h i t e}{\text{XXX}} x - 3 y = 3$

Rearranging the terms of [2]
[3]$\textcolor{w h i t e}{\text{XXX}} x = 3 y + 3$

Substituting $3 y + 3$ for $x$ in [1]
[4]$\textcolor{w h i t e}{\text{XXX}} - 2 \left(3 y + 3\right) + 5 y = - 2$

Simplifying
[5]$\textcolor{w h i t e}{\text{XXX}} - 6 y - 6 + 5 y = - 2$

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

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

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