Final answer:
To solve the system by substitution, we substitute the value of y from one equation into the other equation and solve for x. Then, we substitute the value of x into one of the original equations to find y. The system of equations y = -x - 32 and y = 7x is solved by substitution, yielding the solution x = -4 and y = -28.
Step-by-step explanation:
To solve the system of equations by substitution, we can start by setting the two equations equal to each other:
y = -x - 32
y = 7x
We can substitute the value of y from the second equation into the first equation:
7x = -x - 32
Now we can solve for x:
8x = -32
x = -4
To find the value of y, we substitute x = -4 into either of the original equations:
y = 7(-4)
y = -28
The solution to the system of equations is (x, y) = (-4, -28).