What are the solutions to the system of equations?

Answer:AStep-by-step explanation:Given the 2 equationsy = x² - 4x + 8 → (1)y = 2x + 3 → (2)Since both express y in terms of x we can equate the left sides, that isx² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )x² - 6x + 5 = 0 ← in standard form(x - 1)(x - 5) = 0 ← in factored formEquate each factor to zero and solve for xx - 1 = 0 ⇒ x = 1x - 5 = 0 ⇒ x = 5Substitute these values into (2) for corresponding values of yx = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)Solutions are (1, 5) and (5, 13)