Question

What is the solution(s) for this linear/quadratic system of equations?

Answer 1

Answer:

(3, 7 ) and (2, 2 )

Step-by-step explanation:

Given the 2 equations

y = x² - 2 → (1)

8 = 5x - y → (2)

Rearrange (2) expressing y in terms of x

y = 5x - 8 → (3)

Substitute y = x² - 2 into (3)

x² - 2 = 5x - 8 ← subtract 5x - 8 from both sides

x² - 5x + 6 = 0 ← in standard form

(x - 3)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 2 = 0 ⇒ x = 2

Substitute these values into (3) for corresponding values of y

x = 3 : y = 5(3) - 8 = 15 - 8 = 7 ⇒ (3, 7 )

x = 2 : y = 5(2) - 8 = 10 - 8 = 2 ⇒ (2, 2 )