# How do you solve y = 5x - 10 and y = 3x + 8 using substitution?

Feb 5, 2017

$\left(x , y\right) = \left(9 , 35\right)$
(see below for methodology)

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} y = 5 x - 10$
[2]$\textcolor{w h i t e}{\text{XXX}} y = 3 x + 8$

Using [1] we can substitute $5 x - 10$ for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 5 x - 10 = 3 x + 8$

Simplifying:
[4]$\textcolor{w h i t e}{\text{XXX}} 2 x = 18$

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

We can now use [5] to substitute $9$ for $x$ in [1]
[6]$\textcolor{w h i t e}{\text{XXX}} y = 5 \cdot \left(9\right) - 10$

Simplifying
[7]$\textcolor{w h i t e}{\text{XXX}} y = 35$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We could (and should) verify this result by substituting
$x = 9$ and $y = 35$ in [2]
$\textcolor{w h i t e}{\text{XXX}} 35 = 3 \cdot \left(9\right) + 8$ (correct)