Question

Solve the simultaneous equation: y=x^2+3 y-2x=18

Answer 1

Answer:

(- 3, 12 ) and (5, 28 )

Step-by-step explanation:

Given the 2 equations

y = x² + 3 → (1)

y - 2x = 18 → (2)

Substitute y = x² + 3 into (2)

x² + 3 - 2x = 18 ( subtract 18 from both sides )

x² - 2x - 15 = 0 ← in standard form

(x + 3)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 5 = 0 ⇒ x = 5

Substitute these values into (1) for corresponding values of y

x = - 3 : y = (- 3)² + 3 = 9 + 3 = 12 ⇒ (- 3, 12 )

x = 5 : y = 5² + 3 = 25 + 3 = 28 ⇒ (5, 28 )