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

1 Answer
Mar 18, 2018

Answer:

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]}