94.8k views
3 votes
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.

y = x2 + 5x + 8 y = -x +3 Select the correct choice and fill in any answer boxes in-example-1

1 Answer

2 votes

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:

y = x2 + 5x + 8 y = -x +3 Select the correct choice and fill in any answer boxes in-example-1
User Padix Key
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories