Question

Select all of the points that are solutions to the system of linear inequalities listed below:

10x + 4y < 12
8x - 3y > 20
Options:
A. (3, -8)
B. (2, 5)
C. (-5, 1)
D. (10, 3)
E. (2, -10)

Answer 1

None of the options are solutions to the system of linear inequalities.

Step-by-step explanation:

To find the solutions to the system of linear inequalities, we need to test each option by substituting the values into the inequalities and checking if they satisfy both inequalities. Let's go through each option:

1. A. (3, -8)
   10(3) + 4(-8) = 30 - 32 = -2, which is not less than 12, so it's not a solution to the first inequality.
   8(3) - 3(-8) = 24 + 24 = 48, which is greater than 20, so it satisfies the second inequality.
   Therefore, (3, -8) is not a solution to the system.
2. B. (2, 5)
   10(2) + 4(5) = 20 + 20 = 40, which is less than 12, so it doesn't satisfy the first inequality.
   8(2) - 3(5) = 16 - 15 = 1, which is greater than 20, so it's not a solution to the second inequality.
   Therefore, (2, 5) is not a solution to the system.
3. C. (-5, 1)
   10(-5) + 4(1) = -50 + 4 = -46, which is not less than 12, so it's not a solution to the first inequality.
   8(-5) - 3(1) = -40 - 3 = -43, which is not greater than 20, so it doesn't satisfy the second inequality.
   Therefore, (-5, 1) is not a solution to the system.
4. D. (10, 3)
   10(10) + 4(3) = 100 + 12 = 112, which is less than 12, so it doesn't satisfy the first inequality.
   8(10) - 3(3) = 80 - 9 = 71, which is greater than 20, so it satisfies the second inequality.
   Therefore, (10, 3) is not a solution to the system.
5. E. (2, -10)
   10(2) + 4(-10) = 20 - 40 = -20, which is less than 12, so it doesn't satisfy the first inequality.
   8(2) - 3(-10) = 16 + 30 = 46, which is greater than 20, so it satisfies the second inequality.
   Therefore, (2, -10) is not a solution to the system.