# How do you solve 9x + 7y = -13 and x = 9 - 6y?

Mar 18, 2018

The point of intersection is $\left(- 3 , 2\right)$.

#### Explanation:

$\text{Equation 1} :$ $9 x + 7 y = - 13$

$\text{Equation 2} :$ $x = 9 - 6 y$

This is a system of linear equations. The solutions for $x$ and $y$ represent the point of intersection of the two lines.

I will use substitution to solve for $x$ and $y$.

Equation 2 is already solved for $x$. Substitute $9 - 6 y$ for $x$ in Equation 1 and solve for $y$.

$9 \left(9 - 6 y\right) + 7 y = - 13$

Expand.

$81 - 54 y + 7 y = - 13$

Simplify.

81-47y=-13#

Subtract $81$ from both sides.

$81 - 81 - 47 y = - 13 - 81$

Simplify.

$0 - 47 y = - 94$

$- 47 y = - 94$

Divide both sides by $- 47$.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 47}}}}^{1} y}{{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 47}}}}^{1}} = \frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 94}}}}^{2}}{{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 47}}}}^{1}}$

Simplify

$y = 2$

Substitute $2$ for $y$ in Equation 2 and solve for $x$.

$x = 9 - 6 \left(2\right)$

$x = 9 - 12$

$x = - 3$

The point of intersection is $\left(- 3 , 2\right)$.

graph{(9x+7y+13)(x+6y-9)=0 [-10, 10, -5, 5]}