Question

Which of the following points are solutions to the system of inequalities shown below? Check all that apply.

y > 4x+3 and y < -4x+6
a. (5,5)
b. (3, 15)
c. (-2, 13)
d. (0,5)
e. (3,16)
f. (-2, 14)

Answer 1

The points that are solutions to the system of inequalities are (0,5) and (-2,13).

Step-by-step explanation:

To determine which points are solutions to the system of inequalities, we need to check if each point satisfies both inequalities. Let's check each point one by one:

• (5,5):
  Plugging in the values, we get:
  y > 4x + 3 -> 5 > 4(5) + 3 -> 5 > 20 + 3 -> 5 > 23 (False)
  y < -4x + 6 -> 5 < -4(5) + 6 -> 5 < -20 + 6 -> 5 < -14 (False)
  Hence, (5,5) is not a solution to the given system of inequalities.
• (3, 15):
  Plugging in the values, we get:
  y > 4x + 3 -> 15 > 4(3) + 3 -> 15 > 12 + 3 -> 15 > 15 (False)
  y < -4x + 6 -> 15 < -4(3) + 6 -> 15 < -12 + 6 -> 15 < -6 (False)
  Hence, (3,15) is not a solution to the given system of inequalities.
• (-2, 13):
  Plugging in the values, we get:
  y > 4x + 3 -> 13 > 4(-2) + 3 -> 13 > -8 + 3 -> 13 > -5 (True)
  y < -4x + 6 -> 13 < -4(-2) + 6 -> 13 < 8 + 6 -> 13 < 14 (True)
  Hence, (3,15) is a solution to the given system of inequalities.

Therefore, the points that are solutions to the system of inequalities are (0,5) and (-2,13).