# How do you solve the system using the elimination method for 2x+3y=19 , 8x-3y=-14?

Jul 7, 2015

$\left(x , y\right) = \left(\frac{1}{2} , 6\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$2 x + 3 y = 19$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$8 x - 3 y = - 14$

Add [1] and [2] (eliminating the $y$ term)
[3]$\textcolor{w h i t e}{\text{XXXX}}$$10 x = 5$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{1}{2}$

Substitute $x = \frac{1}{2}$ in [1]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$2 \left(\frac{1}{2}\right) + 3 y = 19$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$3 y = 18$
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 6$