# How do you solve the simultaneous equations y = -2x + 10 and 3x + 5y = 8?

Jul 22, 2015

$\left(x , y\right) = \left(6 , - 2\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 2 x + 10$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$3 x + 5 y = 8$

Substituting $\left(- 2 x + 10\right)$ for $y$ (from [1]) in [2]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$3 x + 5 \left(- 2 x + 10\right) = 8$
Simplifying
[4]$\textcolor{w h i t e}{\text{XXXX}}$$7 x = 42$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = 6$

Substituting $6$ for $x$ back in [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 2 \left(6\right) + 10$
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 2$