Find the volume beneath z = f(x, y) and above the region described by the rectangle with vertices (0,0), (1,0), (1,2), and (0,2). f(x, y)=-x^2-y^2 +c ; use c= 4. hint: compute the double integral required to find the volume under f(x, y) using the limits of integration given by the region on the x-y plane.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.