Question

PLEASE HELP, TIMED FINAL

The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraically are shown in the table.



Which represents the solution(s) of this system of equations?

(–3, –1)
(–3, 5)
(–3, 5) and (–1, 9)
(1, 13) and (3, 20)

Answer 1

(-3, 5) AND (-1, 9)

This is right! I took the edge final, and this was the correct answer! You can also figure out the answer by typing the two equations into a graphing calculator.

I hope this helps!

- sincerelynini

Answer 2

Following on from step 3

0 = (x + 1)(x + 3)

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 3 = 0 ⇒ x = - 3

Substitute these values into either of the 2 equations for the corresponding value of y

using y = 2x + 11

x = - 1 : y = - 2 + 11 = 9 ⇒ (- 1, 9 )

x = - 3 : y = - 6 + 11 = 5 ⇒ (- 3, 5 )

solutions are (- 3, 5 ) and (- 1, 9 )