Select all of the ordered pairs that are solutions to the following system of inequalities.

To determine which ordered pairs are solutions to the given system of inequalities, we need to check each pair against both inequalities:

1. First Inequality: \( y > 5 - 3x \)
2. Second Inequality: \( 6x - 5y < -2 \)

Now, let's check each ordered pair:

a. (3, 7)

1. Check the first inequality: \[ 7 > 5 - 3(3) \implies 7 > 5 - 9 \implies 7 > -4 \quad \text{(True)} \]
2. Check the second inequality: \[ 6(3) - 5(7) < -2 \implies 18 - 35 < -2 \implies -17 < -2 \quad \text{(False)} \] Result: Not a solution.

b. (2, 1)

1. Check the first inequality: \[ 1 > 5 - 3(2) \implies 1 > 5 - 6 \implies 1 > -1 \quad \text{(True)} \]
2. Check the second inequality: \[ 6(2) - 5(1) < -2 \implies 12 - 5 < -2 \implies 7 < -2 \quad \text{(False)} \] Result: Not a solution.

c. (0, 8)

1. Check the first inequality: \[ 8 > 5 - 3(0) \implies 8 > 5 \quad \text{(True)} \]
2. Check the second inequality: \[ 6(0) - 5(8) < -2 \implies 0 - 40 < -2 \implies -40 < -2 \quad \text{(True)} \] Result: This is a solution.

d. (-4, 20)

1. Check the first inequality: \[ 20 > 5 - 3(-4) \implies 20 > 5 + 12 \implies 20 > 17 \quad \text{(True)} \]
2. Check the second inequality: \[ 6(-4) - 5(20) < -2 \implies -24 - 100 < -2 \implies -124 < -2 \quad \text{(True)} \] Result: This is a solution.

Solutions

The pairs that are solutions to the system of inequalities are:

• c. (0, 8)
• d. (-4, 20)