Question
give me a real answer
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
Skip to navigation
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
Skip to navigation
Answers
GPT-4o mini
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.
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.