# How do you solve the simultaneous equations 4x + y = 9  and 2x - y = 3?

Jul 13, 2015

Since both given equations contain similar coefficients for $y$, the simplest method is to add the two equations and solving single variable equations to get
$\left(x , y\right) = \left(2 , 1\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$4 x + y = 9$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$2 x - y = 3$

[3]$\textcolor{w h i t e}{\text{XXXX}}$$6 x = 12$
Divide both sides by $6$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = 2$
Using information from [4], replace $x$ with $2$ in [1]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$4 \left(2\right) + y = 9$
Simplify
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = 1$