What is the solution to the system of equations x2-x+6=y and 2x+2y=36?

X²-x+6=y
2x+2y=36
divide 2nd equation by 2 for ease
x+y=18
subsitute x²-x+6 for y in 2nd equation

x+x²-x+6=18
minus 18 both sides and combine like terms
x²-12=0
add 12 both sides
x²=12
sqrt both sides
x=+/-√12
x=+/-2√3

sub back

x²-x+6=y
try 2√3 then -2√3

2√3
(2√3)²-(2√3)+6=y
12-2√3+6=y
18-2√3=y

other one
-2√3
(-2√3)²-(-2√3)+6=y
12+2√3+6=y
18+2√3=y

solutions are (-2√3,18+2√3) and (2√3,18-2√3)