Final answer:
To solve the system of equations, first simplify -8x - 8y = 0 to x + y = 0 and then combine it with the second equation -5x - 7y = -12 after manipulating to align variables. By elimination, we find y = 1, and then we find x = -1, yielding the solution x = -1 and y = 1.
Step-by-step explanation:
To solve the system of equations -8x - 8y = 0 and -5x - 7y = -12 by combining the equations, we can first simplify the first equation by dividing everything by -8. This gives us x + y = 0, which is Equation (1). Then, we look at the second equation and rewrite it as 5x + 7y = 12, which is Equation (2).
Now, we can multiply Equation (1) by 5 to eliminate x when we add the two equations together. This gives us 5x + 5y = 0. Adding this to Equation (2), 5x + 7y = 12, we get 12y = 12, which simplifies to y = 1.
Using the value of y, we can substitute back into Equation (1) to find x. We now have x + 1 = 0, giving us x = -1. Thus, the solution to the system of equations is x = -1 and y = 1.