# How do you find the solution set for y=6x-5 and y=-x+9?

Aug 11, 2015

$\left\{\begin{matrix}x = 2 \\ y = 7\end{matrix}\right.$

#### Explanation:

Your system of equations looks like this

$\left\{\begin{matrix}y = 6 x - 5 \\ y = - x + 9\end{matrix}\right.$

Notice that $y$ is said to be equal to two distinct expressions that depend on $x$, which can only mean that these expressions must be equal to each other.

$6 x - 5 = - x + 9$

Solve this equation for $x$

$6 x + x = 9 + 5$

$7 x = 14 \implies x = \frac{14}{7} = \textcolor{g r e e n}{2}$

Pick any of the two original equations and find the value of $y$

$y = 6 \cdot \left(2\right) - 5$

$y = 12 - 5 = \textcolor{g r e e n}{7}$

The solution set to this system of equations is

$\left\{\begin{matrix}x = 2 \\ y = 7\end{matrix}\right.$