Solve the following system of equations and show all work. y = −x2 + 4 y = 2x + 1

Y = -x² + 4  (i)
y = 2x + 1  (ii)

From equation (ii), y = 2x + 1. Substitute the value y in equation (i) with 2x + 1.

y = -x² + 4
2x + 1 = -x² + 4
x²+2x+1-4=0
x²+2x-3=0

Solve this quadratic equation using the factor method to get 2 values of x.
x²+2x-3=0
product = -3
sum =2
factors are 3 and -1.
∴x²-x+3x-3=0
  x(x-1)+3(x-1)=0
  (x+3)(x-1)=0
 This means that, 
x+3=0    or x-1=0
x=-3             x=1

For x=-3,                     for x=1
y= 2x + 1                         y = 2x + 1
  =2×-3 + 1                         = 2×1 + 1
 = -5                                    = 3

For x=-3, y=-5              For x=1, y=3                              

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