Question

How do you solve `y=-x^2+2x-3` and y=x-5?

Answer 1

(-1, - 6)
(2, - 3)

Explanation:

`y = - x^2 + 2x -3` ------------------(1)
This is a downward facing U shaped curve
y = x - 5 -------------------------(2)
Straight line cuts it at two points.

Substitute `y = - x^2 + 2x -3` in equation (2)

`- x^2 + 2x -3 = x - 5`
`- x^2 + 2x -3 - x + 5 = 0`
`- x^2 + x + 2 = 0`
`- x^2 + 2x - x + 2 = 0`
x ( - x + 2) + 1 (- x +2) = 0
(x + 1) ( - x + 2) = 0
(x + 1 = 0
x = -1

• x + 2 = 0
  x = 2
  Substitute the x values in equation (1)
  At x = - 1 ; y = -1 - 5 = - 6

(- 1, -6) one point

At x = 2 ; y = 2 - 5 = 3

(2, -3) is another point