Question

Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.

Answer 1

The solution to the system of equations is (0, -3) because that is where the two graphs intersect. It is the only solution since the equations intersect at that point only.

Explanation:

We have the two equations:

`f(x)=|x+1|-4\text{ and } g(x)=-2x-3`

Remember that graphically, the solution(s) of a system of equations is always where the graphs intersect.

We can see that the two graphs intersect at (0, -3).

So, g(0) = -3 and f(0) = -3 also.

And that is the only point of intersection. So the only solution to our system here is (0, -3).