Answer:
Find the solutions below
Explanation:
Given the equation
y = -x^2 + 2x + 7
y = -2x+2
Equating both expressions
-x^2 + 2x + 7 = -2x + 2
-x^2 + 2x + 7 + 2x - 2 = 0
-x^2 + 4x + 5 = 0
Multiply through by -1
x^2 - 4x - 5 = 0
Factorize
x^2 - 5x + x - 5 = 0
x(x-5)+1(x-5) = 0
(x+1)(x-5) = 0
x+1 = 0 and x - 5 = 0
x = -1 and 5
when x = -1
y = -2x+2
y = -2(-1)+2
y = 2+2
y = 4
when x = 5
y = -2(5)+2
y = -10+2
y = -8
Hence the solutions are (-1, 4) and (5, -8)
b) y = x^2-3x-27
y = x - 6
Equating both expressions
x^2-3x-27 = x - 6
x^2-3x-27 - x + 6 = 0
x^2-4x-21 = 0
x^2 - 7x + 3x - 21 = 0
x(x-7)+3(x-7) = 0
(x+3)(x-7) = 0
x = -3 and 7
when x = -3
y = -3-6
y = -9
when x = 7
y = 7 - 6
y = 1
Hence the required solutions are (-3, -9) and (7, 1)