How do you solve -6x + 10y = 5 and -2x + 3y = -1?

Jul 24, 2015

$\left(x , y\right) = \left(\frac{25}{2} , 8\right)$

Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$−6x+10y=5
[2]$\textcolor{w h i t e}{\text{XXXX}}$−2x+3y=−1

Multiply [2] by 3
[3]$\textcolor{w h i t e}{\text{XXXX}}$$- 6 x + 9 x = - 3$

Subtract [3] from [1]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$y = 8$

Substitute $8$ for $y$ in [2]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$- 2 x + 3 \left(8\right) = - 1$

[6]$\textcolor{w h i t e}{\text{XXXX}}$$2 x = 25$

Divide by $2$
[7]$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{25}{2}$