Final answer:
The system of equations is solved by substitution, setting the two expressions for y equal to each other, solving for r, and then using the value of r to find y. The solution to the system is r = -2 and y = 14.
Step-by-step explanation:
To solve the system by substitution, we have two equations where y is expressed in terms of r:
y = -7r
y = 9r + 32
Since both expressions equal y, we can set them equal to each other:
-7r = 9r + 32
We then combine like terms and solve for r:
-7r - 9r = 32
-16r = 32
r = -2
Substitute r back into either of the original equations to solve for y, using y = -7r:
y = -7(-2)
y = 14
Therefore, the solution to the system of equations is r = -2 and y = 14.