# How do you solve the system of equations: x+2y=3, 3x-y= -5?

Aug 5, 2015

$\left(x , y\right) = \left(- 1 , 2\right)$

#### Explanation:

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

Multiply [2] by 2 (so the coefficient of $y$ corresponds to that in [1])
[3]$\textcolor{w h i t e}{\text{XXXX}}$$6 x - 2 y = - 10$

Add [1] and [3] (eliminating the $y$ term)
[4]$\textcolor{w h i t e}{\text{XXXX}}$$7 x = - 7$

Divide [4] by 7
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 1$

Substitute $\left(- 1\right)$ for $x$ in [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$\left(- 1\right) + 2 y = 3$

Add 1 to both sides of [6]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$2 y = 4$

Divide both sides by 2
[8]$\textcolor{w h i t e}{\text{XXXX}}$$y = 2$