Question

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

Answer 1

The point of intersection is `(-3,2)`.

Explanation:

`"Equation 1":` `9x+7y=-13`

`"Equation 2":` `x=9-6y`

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 `9-6y` for `x` in Equation 1 and solve for `y`.

`9(9-6y)+7y=-13`

Expand.

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

Simplify.

81-47y=-13#

Subtract `81` from both sides.

`81-81-47y=-13-81`

Simplify.

`0-47y=-94`

`-47y=-94`

Divide both sides by `-47`.

`(color(red)cancel(color(black)(-47))^1y)/(color(red)cancel(color(black)(-47))^1)=(color(red)cancel(color(black)(-94))^2)/(color(red)cancel(color(black)(-47))^1)`

Simplify

`y=2`

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

`x=9-6(2)`

`x=9-12`

`x=-3`

The point of intersection is `(-3,2)`.

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