Final answer:
To solve the system of equations -3x = -36 + 7y and -3x + 2y = -36, we can use the method of elimination. The equations are identical, which means they represent the same line and have infinitely many solutions.
Step-by-step explanation:
To solve the system of equations -3x = -36 + 7y and -3x + 2y = -36, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the second equation by 7 to make the coefficients of y the same:
-3x + 2y = -36 (1)
-21x + 14y = -252 (2)
Now subtract equation (1) from equation (2) to eliminate x:
-21x + 14y - (-3x + 2y) = -252 - (-36)
-21x + 14y + 3x - 2y = -216
-18x + 12y = -216
Divide the equation by 6 to simplify:
-3x + 2y = -36
-3x + 2y = -36
As we can see, the equations are identical. This means that they represent the same line and have infinitely many solutions. Therefore, the correct answer is:
c. x = 4, y = -6