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

Question

Hazel Anglin · Accepted Answer

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

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

Isaiah Anthony · Answer

undefined To solve the system of equations 9x + 7y = -13 and x = 9 - 6y, you substitute the value of x from the second equation into the first equation and solve for y. Then, you substitute the value of y back into the second equation to solve for x. The solution is x = 4 and y = -1.