Question

Keiko determined that the coordinate points (–4, 0), (–3, –1), and (2, –6) are solutions to the following system. y = − x − 4 y = x 2 + x − 12 Which coordinates from the solution set are reasonable solutions to the system of equations?

Answer 1

only (-4,0) is a reasonable solution.

Explanation:

In order to see which ones are reasonable we need to apply the points to the system and check if they make both equations valid at the same time.

y = -x - 4

y = x² + x - 12

For (-4, 0):

0 = -(-4) - 4 -> 0 = 4 -4 -> 0 = 0 (valid)

0 = (-4)² - 4 - 12 -> 0 = 16 - 16 -> 0 = 0 (valid)

For (-3, -1):

-1 = -(-3) -4 -> -1 = 3 -4 -> -1 = -1 (valid)

-1 = (-3)² -1 - 12 -> -1 = 9 -13 -> -1 = -4 (invalid)

For (2, -6):

2 = -(-6) - 4 -> 2 = 6 -4 -> 2 = 2 (valid)

2 = (-6)² -6 -12 -> 2 = 36 -18 -> 2 = 18 (invalid)

Therefore only (-4,0) is a reasonable solution.