Shafran697
27

# Solve the following system of equations and show all work. y = −x^2 + 4 y = 2x + 1

$\begin{cases} y=-x^{2}+4 \\ y=2x+1 \end{cases} \\ \\ 2x+1=-x^{2}+4 \\ \\ x^{2}+2x-3=0 \\ \\ \Delta=2^{2}-4*1*(-3)=4+12=16 \\ \\ \sqrt{\Delta}=4 \\ \\ x_{1}= \frac{-2-4}{2} =-3 \\ \\ x_{2}= \frac{-2+4}{2}=1 \\ \\ y=2*(-3)+1=-5 \ \vee \ 2*1+1=3$