Determine which of the following points are included in the solution set to the following linear inequality. \[ \begin{array}{l}-3 x+4 y<20\end{array} \] Answer \( \square(-10,7) \) \( \square(0,0) \) \( \square(-1,5) \) \( \square(10,-10) \) \( \square\left(-3, \frac{11}{4}\right) \)

To determine which points satisfy the inequality \(-3x + 4y < 20\), substitute each point \((x, y)\) into the inequality and check if the statement holds true. **Given Inequality:** \[ -3x + 4y < 20 \] **Points to Check:** 1. \((-10, 7)\) 2. \((0, 0)\) 3. \((-1, 5)\) 4. \((10, -10)\) 5. \(\left(-3, \frac{11}{4}\right)\) **Evaluation:** 1. **\((-10, 7)\)** \[ -3(-10) + 4(7) = 30 + 28 = 58 \] \[ 58 < 20 \quad \text{(False)} \] **Does not satisfy the inequality.** 2. **\((0, 0)\)** \[ -3(0) + 4(0) = 0 + 0 = 0 \] \[ 0 < 20 \quad \text{(True)} \] **Satisfies the inequality.** 3. **\((-1, 5)\)** \[ -3(-1) + 4(5) = 3 + 20 = 23 \] \[ 23 < 20 \quad \text{(False)} \] **Does not satisfy the inequality.** 4. **\((10, -10)\)** \[ -3(10) + 4(-10) = -30 - 40 = -70 \] \[ -70 < 20 \quad \text{(True)} \] **Satisfies the inequality.** 5. **\(\left(-3, \frac{11}{4}\right)\)** \[ -3(-3) + 4\left(\frac{11}{4}\right) = 9 + 11 = 20 \] \[ 20 < 20 \quad \text{(False)} \] **Does not satisfy the inequality** (since the inequality is strict). **Conclusion:** Only the points \((0, 0)\) and \((10, -10)\) satisfy the inequality \(-3x + 4y < 20\). **Answer:** Only the points (0, 0) and (10, –10) satisfy –3 x + 4 y < 20.