What is the solution set of y=x? - 5x + 7 and y = 2x + 1?
Separate your x and y values with a comma.
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Does anyone know this?

Respuesta :

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)

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