Answer:
The solutions are (6,13) and (1,3)
Step-by-step explanation:
We want to solve
[tex]y=x^2-5x+7[/tex]
and
[tex]y=2x+1[/tex]
We equate both equations to get:
[tex]x^2-5x+7=2x+1[/tex]
[tex]x^2-5x-2x+7-1=0[/tex]
[tex]x^2-7x+6=0[/tex]
We split the middle term to get:
[tex]x^2-6x-x+6=0[/tex]
[tex]x(x-6)-1(x-6)=0[/tex]
[tex](x-6)(x-1)=0[/tex]
[tex](x-6)=0,(x-1)=0[/tex]
[tex]x=6,x=1[/tex]
When x=6, y=2(6)+1=13
When x=1, y=2(1)+1=3
The solutions are (6,13) and (1,3)