# How do you solve the system using the elimination method for 2x+y=7 and x+2y=11?

Aug 1, 2015

$\left(x , y\right) = \left(1 , 5\right)$
$\textcolor{w h i t e}{\text{XXXX}}$(see below for solution by substitution)

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$2 x + y = 7$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x + 2 y = 11$

Multiply both sides of [1] by $2$ so we have 2 equations with $y$ having a coefficient of $2$
[3]$\textcolor{w h i t e}{\text{XXXX}}$$4 x + 2 y = 14$

Subtract [2] from [3] eliminating the $y$ term
[4]$\textcolor{w h i t e}{\text{XXXX}}$$3 x = 3$

Divide both sides by $3$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = 1$

Substitute $1$ for $x$ in [2]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$1 + 2 y = 11$
Subtract $1$ from both sides
[7]$\textcolor{w h i t e}{\text{XXXX}}$$2 y = 10$
Divide both sides by $2$
[8]$\textcolor{w h i t e}{\text{XXXX}}$$y = 5$