Answer:
(- 2, 1 ) and (1, 4 )
Step-by-step explanation:
Given the 2 equations
y = - x² + 5 → (1)
- x + y = 3 → (2)
Rearrange (2) expressing y in terms of x by adding x to both sides
y = x + 3 → (3)
Substitute y = x + 3 into (1)
x + 3 = - x² + 5 ( subtract - x² + 5 from both sides )
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
Substitute these values into (3) for corresponding values of y
x = - 2 : y = - 2 + 3 = 1 ⇒ (- 2, 1 )
x = 1 : y = 1 + 3 = 4 ⇒ (1, 4 )
