# How do you solve -5x + 14y = 16 ; -3x + 9y = 12?

Jan 2, 2017

$\left(x , y\right) = \left(8 , 4\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} - 5 x + 14 y = 16$
[2]$\textcolor{w h i t e}{\text{XXX}} - 3 x + 9 y = 12$

Multiply each equation by a constant to make coefficients of $x$ inverse of each other.
[2]=[1]$\times \left(- 3\right)$$\textcolor{w h i t e}{\text{XXX}} 15 x - 42 y = - 48$
[3]=[2]$\times 5$$\textcolor{w h i t e}{\text{XXXxx")-15x+49y=color(white)("XX}} 60$

Add [2] and [3] to get rid of $x$ term
[4]$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXX}} 7 y = 28$

Divide both sides of [4] by $7$
[5]$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXX}} y = 4$

Substitute $4$ in place of $y$ in [2] (we could have used [1])
[6]$\textcolor{w h i t e}{\text{XXX}} - 3 x + 9 \cdot 4 = 12$

Simplifying
[7]$\textcolor{w h i t e}{\text{XXX}} - 3 x + 36 = 12$

[8]$\textcolor{w h i t e}{\text{XXX}} - 3 x = - 24$

[9]$\textcolor{w h i t e}{\text{XXX}} x = 8$