How do you solve 6x + 5y = -12 and -9x + y = 69 using substitution?

Jul 9, 2016

(x,y)=color(blue)(""(-7,6))

Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 6 x + 5 y = - 12$
[2]$\textcolor{w h i t e}{\text{XXX}} - 9 x + y = 69$

re-arranging [1]
[3]$\textcolor{w h i t e}{\text{XXX}} y = 9 x + 69$

substituting $\left(9 x + 69\right)$ from [3] for $y$ in [1]
[4]$\textcolor{w h i t e}{\text{XXX}} 6 x + 5 \left(9 x + 69\right) = - 12$

simplifying
[5]$\textcolor{w h i t e}{\text{XXX}} 51 x + 345 = - 12$

[6]$\textcolor{w h i t e}{\text{XXX}} 51 x = - 357$

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

substituting $\left(- 7\right)$ for $x$ in [3]
[8]$\textcolor{w h i t e}{\text{XXX}} y = 9 \cdot \left(- 7\right) + 69 = 6$