Find the solution(s) to the system of equations y = 2 and y = x^2 + 5x + 6.

Answer 1

Happy to help!

A solution to a system of equations means to find the values for x and y where the functions are equal. In this case we have two functions:

y = 2

and

y = x² + 5x + 6

So let's set them equal to each other and see what happens:

2 = x² + 5x + 6

Let's rearrange the equation by subtracting two from each side:

0 = x² + 5x + 4

Does it look familiar yet? It's a quadratic equation! We need to factor this right away...

0 = (x+4)(x+1)

So what values of x make the equation equal zero? Let's try x = -4

0 = (-4 + 4)(-4+1) = 0(-3) = 0

Okay that worked. We could also have found the first solution for x by solving:

x+4 = 0

The second solution can be found by solving:

x+1 = 0

So together, the x values are x = -4 and x = -1. We already know that these values occur at y = 2.

The final answer could be written as (-4, 2) and (-1, 2)

Hope that helps