Question

What is the solution to the following system of equations?
y = x2 + 10x + 11
y = x2 + x − 7

A. (−2, −5)
B. (2, −5)
C. (−2, 5)
D. (2, 5)

Answer 1

You are given that
\(\color{#000000}{ y = x^2 + 10x + 11 }\)
\(\color{#000000}{ y = x^2 + x − 71 }\)

and therefore you can imply by a simple substitution that:
\(\color{#000000}{ x^2 + 10x + 11= x^2 + x − 71 }\)

Answer 2

Then solve the system by first solving this equation (this will give you the x-coordinate of the intersection), and then plug it into one of the original equations (to obtain the y-coordinate of the intersection).

Answer 3

Note: By definition, intersection(s) ((be it points, lines, or planes in \(\mathbb{R}^n\))) are the solution to the system.