# How do you solve the following system?: 2x +y = 13 , 3x +2y = -2

Jan 23, 2016

$\left(x , y\right) = \left(28 , - 43\right)$

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 2 x + y = 13$
[2]$\textcolor{w h i t e}{\text{XXX}} 3 x + 2 y = - 2$

Multiply [1] by $2$ to give $y$ a coefficient equal to that in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x + 2 y = 26$

Subtract [2] from [3] to eliminate the $y$ term
[4]$\textcolor{w h i t e}{\text{XXX}} x = 28$

Substitute $28$ for $x$ back into [1]
[5]$\textcolor{w h i t e}{\text{XXX}} 2 \times 28 + y = 13$

Simplify
[6]$\textcolor{w h i t e}{\text{XXX}} y = 13 - 56 = - 43$

Jan 23, 2016

$x = 28$
$y = - 43$

#### Explanation:

Given -

$2 x + y = 13$ ---------------------------(1)
$3 x + 2 y = - 2$ ---------------------------(2)

Solve equation (1) for $y$

$y = 13 - 2 x$

Substitute $y = 13 - 2 x$ in equation (2)

$3 x + 2 \left(13 - 2 x\right) = - 2$
$3 x + 26 - 4 x = - 2$
$- x + 26 = - 2$
$- x = - 2 - 26$
$- x = - 28$
$x = 28$

Substitute $x = 28$ in equation (1)

$2 \left(28\right) + y = 13$
$56 + y = 13$
$y = 13 - 56 = - 43$
$y = - 43$