Question

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

Answer 1

Answer:

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

Step-by-step 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)

Answer 2

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