Slove the system of equations y=2x-3 y=x^2-3

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

Since both equations express y in terms of x we can equate them

x² - 3 = 2x - 3

subtract 2x from both sides

x² - 2x - 3 = - 3

add 3 to both sides

x² - 2x = 0

take out a common factor of x

x(x - 2) = 0

equate each factor to zero and solve for x

x = 0 or x - 2 = 0 ⇒ x = 2

substitute values of x into y = 2x - 3 for corresponding values of y

x = 0 → y = 0 - 3 = -3 ⇒ (0, -3)

x = 2 → y = 4 - 3 = 1 ⇒ (2, 1)