half o the question asks for the values of x and y if x+y=8

Question

Systems of equations

Answer 1

The first part has the solutions x/y=-2 or -3. So x=-2y or -3y.

Substitute for x in x+y=8: -2y+y=8, -y=8 so y=-8 and x=16; or

-3y+y=8, -2y=8, y=-4 and x=12.

Therefore the solutions are (16,-8) and (12,-4).

If you plug these into the original quadratic you will find that this pair of solutions makes the quadratic = 0.