Solve the system of equations. y = 2x - 3 y = x^2 - 3

(0, - 3) and (2, 1)

Step-by-step explanation:

Given the 2 equations

y = 2x - 3 → (1)

y = x² - 3 → (2)

Substitute y = x² - 3 into (1)

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

x² - 2x = 0 ← factor out x from each term

x (x - 2) = 0

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

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

x = 0 : y = 2 (0) - 3 = 0 - 3 = - 3 ⇒ (0, - 3)

x = 2 : y = 2 (2) - 3 = 4 - 3 = 1 ⇒ (2, 1)