Question

y = x2 + 5x + 8 y = -x +3 Select the correct choice and fill in any answer boxes in your O A. The solution(s) is/are (Type an ordered pair. Use a comma to separate answe B. There is no solution.

Answer 1

To determine whether or not this system has a solution, we proceed as follows:

$-x+3=x^2+5x+8\Rightarrow x^2+6x+5=0$

Now, we use the quadratic function to solve, that is:

$x=\frac{-(6)\pm\sqrt[]{6^2-4(1)(5)}}{2(1)}\Rightarrow\begin{cases}x=-1 \\ x=-5\end{cases}$

From this, we have that the system has two solutions, we determine which replacing x in one of the functions, that is:

$y_1=-(-1)+3\Rightarrow y_1=4$

One solution is the point (-1, 4).

$y_2=-(-5)+3\Rightarrow y_2=8$

And, another solution is the point (-5, 8).

We can see each solution in the following graph: