Question

Solve these pair of simultaneous equations y=x^2-x-1 and y=2-3x

Answer 1

y = x^2 - x - 1
y = 2 - 3x

2 - 3x = x^2 - x - 1
x^2 - x - 1 - 2 + 3x = 0
x^2 + 2x - 3 = 0
(x + 3)(x - 1) = 0

x + 3 = 0 y = 2 - 3x
x = -3 y = 2 - 3(-3)
y = 2 + 9
y = 11

x - 1 = 0 y = 2 - 3x
x = 1 y = 2 - 3(1)
y = 2 - 3
y = -1

so ur solutions are : (-3,11) or (1,-1)

Answer 2

Compare both sides,
x² - x - 1 = 2 - 3x
x² + 2x - 3 = 0
x² -x + 3x - 3 = 0
x(x - 1) 3(x - 1) = 0
(x - 1)(x+3) = 0
x = 1 or - 3

In short, Your Answers would be 1 & -3

Hope this helps!