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)