Final answer:
The solution to the system of equations is x = -16 / 17 and y = 73 / 17.
Step-by-step explanation:
The given system of equations is:
9x - 6y = -20 -- (1)
-3y = 2x - 11 -- (2)
To solve this system of equations, we can use the method of substitution. First, let's solve equation (2) for y:
-3y = 2x - 11
y = (2x - 11) / -3
Now, substitute this expression for y in equation (1):
9x - 6((2x - 11) / -3) = -20
Simplify and solve for x:
9x + 4(2x - 11) = -60
17x - 44 = -60
17x = -60 + 44
17x = -16
x = -16 / 17
Substitute this value of x back into either equation (1) or (2) to solve for y. Let's use equation (2):
-3y = 2(-16 / 17) - 11
-3y = -32 / 17 - 11
-3y = -32 / 17 - 187 / 17
-3y = -219 / 17
y = (-219 / 17) / -3
y = 73 / 17
Therefore, the solution to the system of equations is x = -16 / 17 and y = 73 / 17.