Question

Solve the system of equations. x + y = 15 y = x2 – 5a. (–5, 20) and (4, 11) b. (3, 4) and (7, 8) c. (5, 10) and (–4, 19)d. (5, 20) and (4, 11)

Answer 1

a

Explanation:

x + y = 15 →→ (1)

y = x² - 5 → (2)

substitute y = x² - 5 into (1)

x + x² - 5 = 15 ( subtract 15 froim both sides and arrange into standard form )

x² + x - 20 = 0 ← in standard form

(x + 5)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 4 = 0 ⇒x = 4

substitute these value into (2) for corresponding values of y

x = - 5 → y = (- 5)² - 5 = 25 - 5 = 20

x = 4 → y = 4² - 5 = 16 - 5 = 11

solutions are (- 5, 20 ) and (4, 11 )