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

##### 1 Answer

Sep 6, 2015

(-1, - 6)

(2, - 3)

#### Explanation:

This is a downward facing U shaped curve

y = x - 5 -------------------------(2)

Straight line cuts it at two points.

Substitute

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