# How do you solve by substitution 3y=-1/2x+2 and y=-x+9?

Jun 15, 2015

For the given equations, $\left(x , y\right) = \left(10 , - 1\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$3 y = - \frac{1}{2} x + 2$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$y = - x + 9$

While it is not technically necessary, I find it easier to clear the fractions before actually beginning; so multiplying [1] by $2$
[3]$\textcolor{w h i t e}{\text{XXXX}}$$6 y = - x + 4$

Substituting (from [2]) $\left(- x + 9\right)$ for $y$ in [3]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$6 \left(- x + 9\right) = - x + 4$

Simplifying
[5]$\textcolor{w h i t e}{\text{XXXX}}$$- 6 x + 54 = - x + 4$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$5 x = 50$
[7]$\textcolor{w h i t e}{\text{XXXX}}$$x = 10$

Substituting (from [7]) $10$ for $x$ in [2]
[8]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 10 + 9 = - 1$