"Equation 1":Equation 1: 9x+7y=-139x+7y=−13
"Equation 2":Equation 2: x=9-6yx=9−6y
This is a system of linear equations. The solutions for xx and yy represent the point of intersection of the two lines.
I will use substitution to solve for xx and yy.
Equation 2 is already solved for xx. Substitute 9-6y9−6y for xx in Equation 1 and solve for yy.
9(9-6y)+7y=-139(9−6y)+7y=−13
Expand.
81-54y+7y=-1381−54y+7y=−13
Simplify.
81-47y=-13#
Subtract 8181 from both sides.
81-81-47y=-13-8181−81−47y=−13−81
Simplify.
0-47y=-940−47y=−94
-47y=-94−47y=−94
Divide both sides by -47−47.
(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]}
