What is the y - value of the intersection y=2x and y=x^2-3

y = - 2 or y = 6

Step-by-step explanation:

Given the 2 equations

y = 2x → (1)

y = x² - 3 → (2)

Substitute y = x² - 3 into (1)

x² - 3 = 2x (subtract 2x 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 (1) for corresponding values of y

x = 3 : y = 2 * 3 = 6

x = - 1 : y = 2 * - 1 = - 2