Systems of Inequalities Practice

Question

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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
it.

The other should be a
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 represents the solution set of the given system of inequalities, we need to analyze each inequality and its corresponding graph representation.

1. First Inequality: \( -2x + y \geq 1 \)

   • Rearranging this yields \( y \geq 2x + 1 \).
   • This is a solid line (because the inequality includes "≥") with a slope of 2 and a y-intercept of 1.
   • The region that is shaded should be above the line.

2. Second Inequality: \( y < -12x - 3 \)

   • The line represented by this inequality is dashed because it does not include equality.
   • It has a slope of -12 and a y-intercept of -3.
   • The region that is shaded should be below the line.

Now we analyze the provided graph:

• The graph has a solid line (correct for the first inequality) with a slope of 2 and a y-intercept of 1, shading above the line.
• It also has a dashed line (correct for the second inequality) with a slope of -12 and a y-intercept of -3, shading below the line.

Conclusions

• The first line and its corresponding shading are consistent with the first inequality.
• The second line and its shading are consistent with the second inequality.

Final Answer

Thus, the graph does represent the solution set of the system of inequalities.