What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 3x + 7?A. (–2, 1) and (5, –8)B. (–2, 1) and (–5, –8)C. (2, –3) and (–5, –8)D. (–2, –3) and (–5, –8)

Question

asked Aug 20, 2023 11.0k views

2 Answers

Zawadi · Answer 1 · 2023-08-26T23:42:05+0000

Given

system of equations:

$\begin{gathered} y=-\left(x+2\right)^2+1 \\ y=3x+7 \end{gathered}$

Find

Solutions of the system of equations

Explanation

as we have given

$\begin{gathered} y=-\left(x+2\right)^2+1 \\ y=3x+7 \end{gathered}$

so , from both equations , we obtain

$\begin{gathered} -(x+2)^2+1=3x+7 \\ -(x^2+4+4x)+1=3x+7 \\ -x^2-4x-4+1=3x+7 \\ -x^2-4x-3x-3-7=0 \\ -x^2-7x-10=0 \\ x^2+7x+10=0 \end{gathered}$

now , solve the quadratic equation ,

$\begin{gathered} x^2+7x+10=0 \\ x^2+5x+2x+10=0 \\ x(x+5)+2(x+5)=0 \\ (x+2)(x+5)=0 \\ x=-2,-5 \end{gathered}$

so , when x = -2 then ,

$\begin{gathered} y=3x+7 \\ y=3(-2)+7=1 \end{gathered}$

when x = -5 then

$\begin{gathered} y=3x+7 \\ y=3(-5)+7=-8 \end{gathered}$

Final Answer

Hence , the solutions of the system of equations are (-2 , 1) and (-5 , -8). So , the correct option is B