Determine which of the following points are included in the solution set to the following system of linear inequalities. \[ \begin{array}{c}5 x+3 y>-1 \\ -5 x+y \leq 4\end{array} \] Answer \( \square(-9,-7) \) \( \square(7,-10) \) \( \square(3,19) \) \( \square\left(-4, \frac{19}{3}\right) \) \( \square(0,0) \)

To determine which points are included in the solution set of the given system of inequalities, we'll analyze each point based on the inequalities provided. 1. For point \((-9, -7)\): - Check \(5(-9) + 3(-7) > -1\): \(-45 - 21 > -1 \implies -66 > -1\) (False). - Check \(-5(-9) + (-7) \leq 4\): \(45 - 7 \leq 4 \implies 38 \leq 4\) (False). 2. For point \((7, -10)\): - Check \(5(7) + 3(-10) > -1\): \(35 - 30 > -1 \implies 5 > -1\) (True). - Check \(-5(7) + (-10) \leq 4\): \(-35 - 10 \leq 4 \implies -45 \leq 4\) (True). - This point is in the solution set. 3. For point \((3, 19)\): - Check \(5(3) + 3(19) > -1\): \(15 + 57 > -1 \implies 72 > -1\) (True). - Check \(-5(3) + 19 \leq 4\): \(-15 + 19 \leq 4 \implies 4 \leq 4\) (True). - This point is in the solution set. 4. For point \((-4, \frac{19}{3})\): - Check \(5(-4) + 3(\frac{19}{3}) > -1\): \(-20 + 19 > -1 \implies -1 > -1\) (False). - Check \(-5(-4) + \frac{19}{3} \leq 4\): \(20 + \frac{19}{3} \leq 4\) (False, since \(20\) alone exceeds \(4\)). 5. For point \((0, 0)\): - Check \(5(0) + 3(0) > -1\): \(0 > -1\) (True). - Check \(-5(0) + 0 \leq 4\): \(0 \leq 4\) (True). - This point is in the solution set. In conclusion, the points included in the solution set are \( (7, -10) \), \( (3, 19) \), and \( (0, 0) \). Thus we can mark: \( \square(-9,-7) \) \( \checkmark(7,-10) \) \( \checkmark(3,19) \) \( \square\left(-4, \frac{19}{3}\right) \) \( \checkmark(0,0) \)