# How do you solve the following system: 4x + 7y = 6, 2x + 3y = 34?

Dec 6, 2015

(x,y)=(110,-64)

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 4 x + 7 y = 6$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 y = 34$

Multiply [2] by $2$ to give $x$ the same coefficient as in [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x + 6 y = 68$

Subtract [3] from [1] eliminating the $x$ term
[4]$\textcolor{w h i t e}{\text{XXX}} y = - 62$

Substitute $\left(- 62\right)$ for $y$ in [2] and simplify to solve for $x$
[5]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 \times \left(- 62\right) = 34$

[6]$\textcolor{w h i t e}{\text{XXX}} 2 x - 186 = 34$

[7]$\textcolor{w h i t e}{\text{XXX}} 2 x = 220$

[8]$\textcolor{w h i t e}{\text{XXX}} x = 110$