Final answer:
To solve the system of equations -4x - 4y = 0 and 7x + 5y = 10 using elimination, multiply the equations by appropriate values to make the coefficients of x or y cancel out when added together. Find the value of y and then substitute it back into one of the equations to find the value of x.
Step-by-step explanation:
To solve the system of equations -4x - 4y = 0 and 7x + 5y = 10 using elimination, we can multiply the first equation by 7 and the second equation by -4 so that the coefficients of x in both equations will cancel out when added together. This gives us:
-28x - 28y = 0
-28x - 20y = -40
Adding these equations gives us -48y = -40. Dividing both sides by -48 gives us y = 5/6. Substituting this value of y back into the first equation gives us -4x - 4(5/6) = 0. Simplifying this equation gives us x = -5/6.
Therefore, the solution to the system of equations is x = -5/6 and y = 5/6.