Question

In the following exercises, solve the system of equations by using substitution.

$$\begin{gathered} y=x^2+3 \\ y=-2x+2 \end{gathered}$$

Short answer

Solution for the system of equations

$$\begin{gathered} \hspace{0.17em}x=-1 \\ y=4 \end{gathered}$$

Step-by-step solution

Given information 

System of equations

$$\begin{gathered} y=x^2+3 \\ y=-2x+2 \end{gathered}$$

Substitution method 

$$\begin{gathered} y=x^2+3 \\ y=-2x+2 \end{gathered}$$

Substitute y =-2x+2 in first equation

$$\begin{gathered} -2x+2=x^2+3 \\ Add2xandsubtract2frombothsides \\ 0=x^2+3+2x-2 \\ 0=x^2+2x+1 \\ 0=(x+1)(x+1) \\ x+1=0 \\ x=-1 \end{gathered}$$

Substitute x value 

substitute x=-1 in the second equation

$$\begin{gathered} y=-2x+2 \\ y=-2(-1)+2 \\ y=4 \end{gathered}$$

Step 4:

solution for the given system of equations

$x=-1,y=4$