Question
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Writing Simultaneous Linear Equations Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
Two lines slope upward on a coordinate plane. A solid line passes through the plotted point left parenthesis 2 comma 7 right parenthesis. A dotted line intersects the first line at the plotted point left parenthesis negative 1 comma 1 right parenthesis.
What is the system of equations shown in the graph?
(1 point)
Responses
{y=−x+1y=2x+7
enlarged left brace start layout first row y equals negative x plus 1 second row y equals 2 x plus 7 end layout
{y=3x+2y=4x+3
enlarged left btrace start layout first row y equals 3 x plus 2 second row y equals 4 x plus 3 end layout
{y=2x−3y=3x−4
enlraged left brace start layout first row y equals 2 x minus 3 second row y equals 3 x minus 4 end layout
{y=2x+3y=3x+4
enlarged left brace start layout first row y equals 2 x plus 3 second row y equals 3 x plus 4 end layout
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Writing Simultaneous Linear Equations Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
Two lines slope upward on a coordinate plane. A solid line passes through the plotted point left parenthesis 2 comma 7 right parenthesis. A dotted line intersects the first line at the plotted point left parenthesis negative 1 comma 1 right parenthesis.
What is the system of equations shown in the graph?
(1 point)
Responses
{y=−x+1y=2x+7
enlarged left brace start layout first row y equals negative x plus 1 second row y equals 2 x plus 7 end layout
{y=3x+2y=4x+3
enlarged left btrace start layout first row y equals 3 x plus 2 second row y equals 4 x plus 3 end layout
{y=2x−3y=3x−4
enlraged left brace start layout first row y equals 2 x minus 3 second row y equals 3 x minus 4 end layout
{y=2x+3y=3x+4
enlarged left brace start layout first row y equals 2 x plus 3 second row y equals 3 x plus 4 end layout
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Answers
GPT-4o mini
To determine the system of equations from the description of the graph, let's analyze the information provided:
1. We have two lines on a coordinate plane.
2. The first line is solid and passes through the point (2, 7).
3. The second line is dotted and intersects the first line at the point (-1, 1).
From the details, we can gather the following:
- The solid line must be the one that has a defined point (2, 7), and we need to find the equation for that line. Given that it has a positive slope and the y-value is 7 when x is 2, we should identify the correct linear equation that would fit this requirement.
- Similarly, the dotted line intersects the solid line at (-1, 1), and we need its equation too.
To find the equations of the solid line and the dotted line, we can check each system of equations provided in the options:
1. **{y = -x + 1; y = 2x + 7}**
- The equation y = 2x + 7 can be rearranged. When x=2, y=2(2)+7=11 (not matching (2,7)).
2. **{y = 3x + 2; y = 4x + 3}**
- The first equation (3x + 2) at x=2 gives y=3(2)+2=8 (not matching (2,7)). The second does not match either.
3. **{y = 2x - 3; y = 3x - 4}**
- The first equation (2x - 3) gives (2, 1) at x=2; the second does not match (2,7).
4. **{y = 2x + 3; y = 3x + 4}**
- The first equation (2x + 3) gives (2,7) when x=2.
- Testing the second equation at (-1): y=3(-1)+4=1, which matches the intersection point (-1,1).
Only the last system **{y = 2x + 3; y = 3x + 4}** is consistent with the described graph.
Thus, the correct system of equations that corresponds to the graph is:
**{y = 2x + 3; y = 3x + 4}**
1. We have two lines on a coordinate plane.
2. The first line is solid and passes through the point (2, 7).
3. The second line is dotted and intersects the first line at the point (-1, 1).
From the details, we can gather the following:
- The solid line must be the one that has a defined point (2, 7), and we need to find the equation for that line. Given that it has a positive slope and the y-value is 7 when x is 2, we should identify the correct linear equation that would fit this requirement.
- Similarly, the dotted line intersects the solid line at (-1, 1), and we need its equation too.
To find the equations of the solid line and the dotted line, we can check each system of equations provided in the options:
1. **{y = -x + 1; y = 2x + 7}**
- The equation y = 2x + 7 can be rearranged. When x=2, y=2(2)+7=11 (not matching (2,7)).
2. **{y = 3x + 2; y = 4x + 3}**
- The first equation (3x + 2) at x=2 gives y=3(2)+2=8 (not matching (2,7)). The second does not match either.
3. **{y = 2x - 3; y = 3x - 4}**
- The first equation (2x - 3) gives (2, 1) at x=2; the second does not match (2,7).
4. **{y = 2x + 3; y = 3x + 4}**
- The first equation (2x + 3) gives (2,7) when x=2.
- Testing the second equation at (-1): y=3(-1)+4=1, which matches the intersection point (-1,1).
Only the last system **{y = 2x + 3; y = 3x + 4}** is consistent with the described graph.
Thus, the correct system of equations that corresponds to the graph is:
**{y = 2x + 3; y = 3x + 4}**