How do you solve the following system: 3x - 2y = 9, 2x + 3y = 34?

Jan 16, 2016

$\left(x , y\right) = \left(\frac{95}{13} , \frac{84}{13}\right)$

Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x - 2 y = 9$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 y = 34$

Multiply [1] by 3 and [2] by 2 to get equivalent coefficients for $y$
[3]$\textcolor{w h i t e}{\text{XXX}} 9 x - 6 y = 27$
[4]$\textcolor{w h i t e}{\text{XXX}} 6 x + 6 y = 68$

[5]$\textcolor{w h i t e}{\text{XXX}} 13 x = 95$

Divide both sides by 13
[6]$\textcolor{w h i t e}{\text{XXX}} x = \frac{95}{13}$

Substitute $13$ for $x$ in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} 3 \cdot \left(\frac{95}{13}\right) - 2 y = 9$

Simplify
[8]$\textcolor{w h i t e}{\text{XXX}} 2 y = \frac{285}{13} - 9 = \frac{285 - 117}{13} = \frac{168}{13}$

[9]$\textcolor{w h i t e}{\text{XXX}} y = \frac{84}{13}$