sub x^2+12x+10 for y in other equaiton
-8x+x^2+12x+10=10
x^2+4x+10=10
minus 10 both sides
x^2+4x=0
factor
(x+4)(x)=0
set to zer
x+4=0
x=-4
x=0
x=-4 or 0
sub back
y=0^2+12(0)+10, y=10
(0,10)
y=(-4)^2+12(-4)+10, y=-22
(-4,-22)
solutions are
(0,10) and (-4,-22)