Question

What is the solution set of y = x2 + 2x + 7 and y = x + 7? A. {(0, 7), (-1, 6)} B. {(0, 7), (-7, 0)} C. {(0, 7), (1, 8)} D. {(-2, 0), (4, 0)}

Answer 1

A.

Explanation:

If

`y=x^2+2x+7` AND

y = x + 7, then by the transitive property of equality:

`x^2+2x+7=x+7`

We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:

`x^2+x=0`

We can factor out the common x to get:

x(x + 1) = 0

which tells us by the Zero Product Property that either

x = 0 and/or x + 1 = 0 and x = -1

We are expecting 2 solutions for x since this is a second degree polynomial. We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y

y = 0 + 7 so

y = 7 and the coordinate is (0, 7)

y = -1 + 7 so

y = 6 and the coordinate is (-1, 6)