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)