Answer:
Step-by-step explanation:
y = x² - 13x + 57 -------(i)
y = 2x + 3 ------------- (ii)
Substitute y = 2x + 3 in equation (i)
2x + 3 = x² - 13x + 57
x² - 13x + 57 = 2x + 3
x² - 13x + 57 - 2x -3 = 0 (Write like terms together}
x² - 13x -2x + 57 -3 = 0
x² - 15x + 54 = 0
Sum = - 15
Product = 54
Factors = 9 * 6
x² - 15x + 54 = 0
x² - 9x - 6x + (-9)*(-6) = 0
x (x-9) -6(x - 9) = 0
(x - 9)(x-6) = 0
x - 9 = 0 ; x - 6 = 0
x = 9 ; x = 6
x = 9 or 6
When x = 9; y = 2*9 + 3 = 18 +3 = 21
When x = 6,; y = 2*6 + 3 = 12 + 3 = 15
(x,y) = (9,21) or (6,15)
