\( \left.\begin{array}{l}\text { Correct } \\ \text { Determine which of the following points are included in the solution set to the following system of linear inequalities. } \\ \qquad \begin{array}{l}4 x+2 y>-3 \\ -2 x+y \leq 2\end{array} \\ \text { Answer } \\ \square(5,7) \\ \square(-7,-5) \\ \square\left(-1, \frac{1}{2}\right) \\ \square(8,0)\end{array}\right] \)

To determine whether the points are included in the solution set of the system of inequalities, we can test each point by substituting \( (x, y) \) into both inequalities. 1. For the point \( (5, 7) \): - \( 4(5) + 2(7) = 20 + 14 = 34 \) which is greater than -3 (True). - \( -2(5) + 7 = -10 + 7 = -3 \) which is not less than or equal to 2 (False). - So, \( (5, 7) \) is **not** in the solution set. 2. For the point \( (-7, -5) \): - \( 4(-7) + 2(-5) = -28 - 10 = -38 \) which is not greater than -3 (False). - \( -2(-7) + (-5) = 14 - 5 = 9 \) which is greater than 2 (False). - So, \( (-7, -5) \) is **not** in the solution set. 3. For the point \( \left(-1, \frac{1}{2}\right) \): - \( 4(-1) + 2\left(\frac{1}{2}\right) = -4 + 1 = -3 \) which is not greater than -3 (False). - \( -2(-1) + \frac{1}{2} = 2 + 0.5 = 2.5 \) which is greater than 2 (False). - So, \( \left(-1, \frac{1}{2}\right) \) is **not** in the solution set. 4. For the point \( (8, 0) \): - \( 4(8) + 2(0) = 32 + 0 = 32 \) which is greater than -3 (True). - \( -2(8) + 0 = -16 \) which is not less than or equal to 2 (False). - So, \( (8, 0) \) is **not** in the solution set. **Final answers**: - \( (5, 7) \): ☐ - \( (-7, -5) \): ☐ - \( \left(-1, \frac{1}{2}\right) \): ☐ - \( (8, 0) \): ☐ All tested points do not satisfy the inequalities; hence, none are included in the solution set.