Question

What are the solutions to the system
y=x^2-6x+7
y=-x+13

Answer 1

I've attached the graphs to this answer. I hope they help. 

Answer 2

The solutions are (-1, 14) and (6, 7)

Explanation:

Given two equations

`y=x^2-6x+7.......(1)`

`y=-x+13...............(2)`

we have to solve the above two equations

Substitute the value of y from (2) equation to (1), we get

`-x+13=x^2-6x+7`

`x^2-5x-6=0`

By middle term splitting method

`x^2-6x+x-6=0`

`x(x-6)+1(x-6)=0`

`(x+1)(x-6)=0`

`x=-1,6`

(2) ⇒ y=-x+13

when x=-1, y=-(-1)+13=1+13=14

when x=6, y=-6+13=7

Hence, the solutions are (-1, 14) and (6, 7)