set 5x-9 = [tex] x^{2} [/tex] - 3x + 7
⇒ 0 = [tex] x^{2} [/tex] - 8x + 16
⇒ factoring we get... 0 = (x-4)² so the x-coordinate for the solution is x = 4
To find the y-coordinate, plug x = 4 into one of the equations (you can plug it into both just to make sure you're right).
y = 5x - 9 plug in x = 4 ⇒ y = 5(4) - 9 = 20 - 9 = 11
y = [tex] x^{2} [/tex] - 3x + 7 plug in x = 4 ⇒ y = (4)² - 3(4) + 7 = 16 - 12 + 7 = 11
∴ The solution to the system is (4, 11) which has y-coordinate 11.
