# How do you solve the system using the elimination method for 9x - 9y = 27 and 7y - 3x = -11?

Jul 9, 2015

$\left(x , y\right) = \left(\frac{5}{2} , - \frac{1}{2}\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$9 x - 9 y = 27$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$7 y - 3 x = - 11$

Resequence the terms of [2] so the variables occur in the same order as in [1]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$- 3 x + 7 y = - 11$

Multiply [3] by $3$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$- 9 x + 21 y = - 33$

[5]$\textcolor{w h i t e}{\text{XXXX}}$$12 y = - 6$

Divide [5] by$12$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = - \frac{1}{2}$

Substitute $y = - \frac{1}{2}$ into [1]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$9 x - 9 \left(- \frac{1}{2}\right) = 27$

Simplifying
[8]$\textcolor{w h i t e}{\text{XXXX}}$$9 x = \frac{45}{2}$

[9]$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{5}{2}$