Answer:
x = 3, y = 5
Explanation:
y =4x - 7
y = x² -2x + 2
so 4x - 7 = x² -2x + 2
subtract 4x from both sides and add 7 to both sides:
0 = x² -2x + 2 - 4x + 7
x² -6x + 9 = 0.
use the quadratic formula (can also factorise or complete the square):
x = ((-b ± √(b² - 4ac)) ÷ 2a)
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
NB number in front of x ² is just one. When no number is presented in front, it is just a 1. In this case, it is 1 x ² (simply just one lot of x ², or just x ²).
x = [(-b ± √(b² - 4ac)) ÷ 2a]
a = 1, b = -6, c = 9.
x = [(-(-6) ± √((-6)² - 4(1)(9))) ÷ 2(1)]
= [(6 ± √(36 - 36)) ÷ 2]
= [(6 ± 0) ÷ 2]
= 3.
there are two roots, 3. why only 3? because 3 is a 'repeated root.' it's repeated, so there are two roots.
(x - 3) (x - 3) = x² - 3x - 3x + 3X3
= x² - 6x + 9 (exactly the equation we began with).
y = 4x - 7
= 4(3) - 7
= 12 - 7
= 5.
so, x = 3 and y = 5