To determine whether the graph accurately represents the solution set of the given system of inequalities, let's analyze each inequality:
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For the first inequality: \(-2x + y \geq 1\)
Rearranging this, we have: \[ y \geq 2x + 1 \]
- The slope is \(2\).
- The y-intercept is \(1\).
- Since the inequality is "greater than or equal to," the line should be solid, and the shading should be above the line.
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For the second inequality: \(y < -\frac{1}{2}x - 3\)
Rearranging this gives: \[ y < -\frac{1}{2}x - 3 \]
- The slope is \(-\frac{1}{2}\).
- The y-intercept is \(-3\).
- Since the inequality is "less than," the line should be dashed, and the shading should be below the line.
Analyzing the Graph:
- The first inequality is represented by a solid line with a slope of \(2\) and a y-intercept of \(1\), which seems to match correctly with the shading above the line.
- The second inequality is represented by a dashed line but with a slope of \(-12\), which does not correspond to the correct second inequality. In fact, the correct slope for the second line should be \(-\frac{1}{2}\), not \(-12\).
Conclusion:
Thus, the graph does not represent the solution set of the system of inequalities, since the second inequality is represented incorrectly.
Final Answers to Select:
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One should be a solid line, with a slope of 2, a y-intercept of 1, and shading above it.
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The other should be a dashed line, with a slope of -1/2, a y-intercept of -3, and shading below it.
So, the graph does not represent the solution set of the system of inequalities.