Question

y = x2 + 2x + 6 y = -x + 4 Select the correct choice and fill in any answer boxes in your choice below. O A. The solution(s) is/are (Type an ordered pair Use a comma to separate answers as needed.) O B. There is no solution

Answer 1

Given the system of equations:

`\begin{gathered} y=x^2+2x+6 \\ y=-x+4 \end{gathered}`

Using the substitution :

So,

`x^2+2x+6=-x+4`

Solve for x:

`\begin{gathered} x^2+2x+6=-x+4 \\ x^2+2x+x+6-4=0 \\ x^2+3x+2=0 \end{gathered}`

Factor the last equation :

`\begin{gathered} x^2+3x+2=0 \\ (x+1)(x+2)=0 \\ x+1=0,x+2=0 \\ x=-1\text{or x = -2} \end{gathered}`

So, the answer is option A

The solutions are: x = -1 , -2

y = 5 , 6

As order pairs , the solution will be : ( -1 , 5 ) and ( -2 , 6 )

The following image represents the graphical solution of the system