# How do you solve the simultaneous equations 3x + 4y = 7 and 5x - 2y = 16?

Jul 22, 2015

$\left(x , y\right) = \left(3 , - \frac{1}{2}\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$3 x + 4 y = 7$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$5 x - 2 y = 16$

Multiply [2} by 2 giving
[3]$\textcolor{w h i t e}{\text{XXXX}}$$10 x - 4 y = 32$

[4]$\textcolor{w h i t e}{\text{XXXX}}$$13 x = 39$

Divide both sides by 13
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = 3$

Substitute $3$ for $x$ in [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$3 \left(3\right) + 4 y = 7$

Simplify
[7]$\textcolor{w h i t e}{\text{XXXX}}$$4 y = - 2$

[8]$\textcolor{w h i t e}{\text{XXXX}}$$y = - \frac{1}{2}$