Which point would not be a solution to the system of linear inequalities shown below? ygt 3x-7 y+xgeqslant -1

To determine which point would not be a solution to the system of linear inequalities, we need to test each point against both inequalities.<br /><br />The given system of linear inequalities is:<br />1. \( y > 3x - 7 \)<br />2. \( y + x \geq -1 \)<br /><br />Let's test each point:<br /><br />### Point A: (0, 0)<br />1. For \( y > 3x - 7 \):<br /> \[<br /> 0 > 3(0) - 7 \implies 0 > -7 \quad \text{(True)}<br /> \]<br />2. For \( y + x \geq -1 \):<br /> \[<br /> + 0 \geq -1 \implies 0 \geq -1 \quad \text{(True)}<br /> \]<br /><br />### Point B: (1, 4)<br />1. For \( y > 3x - 7 \):<br /> \[<br /> 4 > 3(1) - 7 \implies 4 > -4 \quad \text{(True)}<br /> \]<br />2. For \( y + x \geq -1 \):<br /> \[<br /> 4 + 1 \geq -1 \implies 5 \geq -1 \quad \text{(True)}<br /> \]<br /><br />### Point C: (-1, -2)<br />1. For \( y > 3x - 7 \):<br /> \[<br /> -2 > 3(-1) - 7 \implies -2 > -10 \quad \text{(True)}<br /> \]<br />2. For \( y + x \geq -1 \):<br /> \[<br /> -2 + (-1) \geq -1 \implies -3 \geq -1 \quad \text{(False)}<br /> \]<br /><br />### Point D: (2, 1)<br />1. For \( y > 3x - 7 \):<br /> \[<br /> 1 > 3(2) - 7 \implies 1 > -1 \quad \True)}<br /> \]<br />2. For \( y + x \geq -1 \):<br /> \[<br /> 1 + 2 \geq -1 \implies 3 \geq -1 \quad \text{(True)}<br /> \]<br /><br />### Conclusion<br />The point that does not satisfy both inequalities is Point C: (-1, -2).