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

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  (x, y) = (-3, -5) and (1, 3)

Step-by-step explanation:

Equate the expressions for y.

  -x^2 +4 = 2x +1

  4 = x^2 +2x +1 . . . . . add x^2

  4 = (x +1)^2 . . . . . . . . rewrite as square

  ±2 = x +1 . . . . . . . . . . take square root

  x = -1 ±2 = {-3, 1} . . . . subtract 1

  y = 2x +1 = 2{-3, 1} +1 = {-6, 2} +1 = {-5, 3} . . . . find corresponding y-values

The solutions are ...

  (x, y) = (-3, -5) and (1, 3)

(- 3, - 5 ) and (1, 3 )

Step-by-step explanation:

Given the 2 equations

y = - x² + 4 → (1)

y = 2x + 1 → (2)

Substitute y = 2x + 1 into (1)

2x + 1 = - x² + 4 ( subtract - x² + 4 from both sides )

x² + 2x - 3 = 0 ← in standard form

(x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for corresponding values of y

x = - 3 : y = 2(- 3) + 1 = - 6 + 1 = - 5 ⇒ (- 3, - 5 )

x = 1 : y = 2(1) + 1 = 2 + 1 = 3 ⇒ (1, 3 )

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step-by-step explanation: