Solve the following system of equations and show all work.

y = -x^2 + 4
y = 2x + 1

-x^2 + 4 = 2x + 1
-x^2 - 2x + 4 - 1 = 0
-x^2 - 2x + 3 = 0
(x + 3)(-x + 1)= 0

x + 3 = 0           -x + 1 = 0
x = -3                -x = -1
                          x = 1

so x = -3 and x = 1

Set them equal since they both equatl y
-x^2+4=2x+1
add x^2-4 to both sides
0=x^2+2x-3
factor
0=(x-1)(x+2)
set each to zero
x-1=0
x=1

x+2=0
x=-2

x=1 or -2

sub them
y=2(1)+1
y=2+1
y=3

y=2(-2)+1
y=-4+1
y=-3

x is 1 and y is 3 or
x is -2 and y is -3

solutions are
(1,3) and (-2,-3)