# How do you solve the system of equations 14x - 9y = 2 and x - 9y = - 50?

Dec 8, 2016

(x,y)=color(green)(""(4,6))

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 14 x - 9 y = 2$
[2]$\textcolor{w h i t e}{\text{XXX}} x - 9 y = - 50$

Subtraction [2] from [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 13 x = 52$

Dividing both sides of [3] by $13$
[4]$\textcolor{w h i t e}{\text{XXX}} x = 4$

Substituting $4$ for $x$ in [2]
[5]$\textcolor{w h i t e}{\text{XXX}} 4 - 9 y = - 50$

Subtracting $4$ from both sides of [5]
[6]$\textcolor{w h i t e}{\text{XXX}} - 9 y = - 54$

Dividing both sides of [6] by $\left(- 9\right)$
[7]$\textcolor{w h i t e}{\text{XXX}} y = 6$