Question

4 which ordered pair is not in the solution set of $y > -\frac{1}{2}x + 5$ and $y \leq 3x - 2$?

1. (5,3)
2. (4,3)
3. (3,4)
4. (4,4)

Explanation:

Step1: Test (5,3) in inequalities

First inequality: $3 > -\frac{1}{2}(5) + 5 = -\frac{5}{2} + 5 = \frac{5}{2} = 2.5$ (true)
Second inequality: $3 \leq 3(5) - 2 = 15 - 2 = 13$ (true)

Step2: Test (4,3) in inequalities

First inequality: $3 > -\frac{1}{2}(4) + 5 = -2 + 5 = 3$ (false, 3 is not greater than 3)
Second inequality: $3 \leq 3(4) - 2 = 12 - 2 = 10$ (true)

Step3: Test (3,4) in inequalities

First inequality: $4 > -\frac{1}{2}(3) + 5 = -\frac{3}{2} + 5 = 3.5$ (true)
Second inequality: $4 \leq 3(3) - 2 = 9 - 2 = 7$ (true)

Step4: Test (4,4) in inequalities

First inequality: $4 > -\frac{1}{2}(4) + 5 = -2 + 5 = 3$ (true)
Second inequality: $4 \leq 3(4) - 2 = 12 - 2 = 10$ (true)

Answer:

1. (4,3)