Question

Which of the following points shows a solution to the simultaneous inequalities y>1/2x+5 and y<−2x+1?
(1 point)

(-1.6,4.2)

(-5,5)

(4,8)

(1,5.5)

Answer 1

Check each point against y > (1/2)x + 5 and y < −2x + 1:

- (-1.6, 4.2): (1/2)(-1.6)+5 = 4.2, but 4.2 is not > 4.2 → fails.
- (-5, 5): (1/2)(-5)+5 = 2.5 and -2(-5)+1 = 11. 5 > 2.5 and 5 < 11 → satisfies both.
- (4, 8): (1/2)(4)+5 = 7 and -2(4)+1 = -7. 8 > 7 but 8 < -7 is false → fails.
- (1, 5.5): (1/2)(1)+5 = 5.5, but 5.5 is not > 5.5 → fails.

Answer: (-5, 5).