How do you solve the system using the elimination method for 3a + 4b = 2 and 4a - 3b = -14?

Jul 8, 2015

$\left(a , b\right) = \left(- 2 , 2\right)$

Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXXX}}$$3 a + 4 b = 2$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$4 a - 3 b = - 14$

Multiply [1] by 4 and [2] by 3 to obtain two equations with the same $a$ coefficient
[3]$\textcolor{w h i t e}{\text{XXXX}}$$12 a + 16 b = 8$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$12 a - 9 b = - 42$

Subtract [4] from [3] to clear the $a$ term
[5]$\textcolor{w h i t e}{\text{XXXX}}$25b= 50#

Divide both sides by $25$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$b = 2$

Substitute $b = 2$ into equation [1]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$3 a + 4 \left(2\right) = 2$

[8]$\textcolor{w h i t e}{\text{XXXX}}$$3 a = - 6$

[9]$\textcolor{w h i t e}{\text{XXXX}}$$a = - 2$