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.