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Question

Does the graph represent the solution set of the system of inequalities?

−2x+y≥1


y<−12x−3


Use the image to answer the question.

The coordinate grid has x and y axes labeled from negative 5 to 5. The graph of a solid line goes through the points negative 1, negative 1; 0, 1; and 1, 3. There is shading above the line. The graph of a dashed line goes through the points negative 4, negative 1; 0, negative 3; and 2, negative 4. There is shading below the line.

Select the correct answers from the lists.

(2 points)
One should be a solid line, with a slope of 2, a y-intercept of 1, and shading
above
it.

The other should be a
solid
line, with a slope of −12
, a y-intercept of −3
, and shading
it.

So, the graph
represent the solution set of the system of inequalities.

Remaining Attempts : 3
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Answer 1

To determine whether the graph accurately represents the solution set of the given system of inequalities, let's analyze each inequality:

1. 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.

2. 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:

1. One should be a solid line, with a slope of 2, a y-intercept of 1, and shading above it.

2. 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.