9514 1404 393
Answer:
(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)
Answer:
(- 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 )
