Question

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?

Answer 1

The solutions are (6,13) and (1,3)

Explanation:

We want to solve

`y=x^2-5x+7`

and

`y=2x+1`

We equate both equations to get:

`x^2-5x+7=2x+1`

`x^2-5x-2x+7-1=0`

`x^2-7x+6=0`

We split the middle term to get:

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

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

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

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

`x=6,x=1`

When x=6, y=2(6)+1=13

When x=1, y=2(1)+1=3

The solutions are (6,13) and (1,3)