Question
Which of the graphs with no solution correctly shows the system of equations y=2x+4 and −2x+y=8?(1 point)
Responses
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 8 right parenthesis.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Skip to navigation
Responses
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 8 right parenthesis.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 4 right parenthesis and left parenthesis negative 2 comma 0 right parenthesis. The dashed lines pass through left parenthesis 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The dashed lines pass through left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 8 right parenthesis.
Skip to navigation
Answers
Answer
So which one is it?
Answered by
GPT-4o mini
To determine which graph represents a system of equations with no solution, we need to analyze the given equations:
1. \( y = 2x + 4 \)
2. \( -2x + y = 8 \)
First, we can rewrite the second equation in a similar slope-intercept form:
\[
y = 2x + 8
\]
Now, we can compare the two equations:
1. \( y = 2x + 4 \)
2. \( y = 2x + 8 \)
Both lines have the same slope (2) but different y-intercepts (4 and 8), meaning that they are parallel lines. Parallel lines will never intersect, indicating that there is no solution to this system of equations.
Now, based on this information, we need to identify which graph shows two parallel lines:
- Look for a graph where both lines have the same slope (parallel) and don't intersect.
- The correct graph should show one line with a y-intercept of 4 (like the first equation) and another line with a y-intercept of 8 (or any value other than 4 that maintains parallelism).
In summary, the graph that depicts two parallel lines with the described characteristics represents the system of equations with no solution. Choose the option that has parallel lines with the correct slopes and intercept values based on the equations we analyzed.
1. \( y = 2x + 4 \)
2. \( -2x + y = 8 \)
First, we can rewrite the second equation in a similar slope-intercept form:
\[
y = 2x + 8
\]
Now, we can compare the two equations:
1. \( y = 2x + 4 \)
2. \( y = 2x + 8 \)
Both lines have the same slope (2) but different y-intercepts (4 and 8), meaning that they are parallel lines. Parallel lines will never intersect, indicating that there is no solution to this system of equations.
Now, based on this information, we need to identify which graph shows two parallel lines:
- Look for a graph where both lines have the same slope (parallel) and don't intersect.
- The correct graph should show one line with a y-intercept of 4 (like the first equation) and another line with a y-intercept of 8 (or any value other than 4 that maintains parallelism).
In summary, the graph that depicts two parallel lines with the described characteristics represents the system of equations with no solution. Choose the option that has parallel lines with the correct slopes and intercept values based on the equations we analyzed.
Answered by
GPT-4o mini
Based on the equations we analyzed:
1. \( y = 2x + 4 \) has a slope of 2 and a y-intercept of 4.
2. \( y = 2x + 8 \) has a slope of 2 and a y-intercept of 8.
We are looking for a graph with two parallel lines.
Among the descriptions of the graphs provided, the correct graph showing the system of equations with no solution (two parallel lines) is:
**The first graph** (the one showing a solid line through (0, 4) and (-2, 0) and a dashed line through (-4, 0) and (0, 8)).
This graph correctly represents the two equations as parallel lines:
- The solid line (y = 2x + 4) passes through (0, 4).
- The dashed line (y = 2x + 8) passes through (0, 8).
Thus, the first option is the correct choice.
1. \( y = 2x + 4 \) has a slope of 2 and a y-intercept of 4.
2. \( y = 2x + 8 \) has a slope of 2 and a y-intercept of 8.
We are looking for a graph with two parallel lines.
Among the descriptions of the graphs provided, the correct graph showing the system of equations with no solution (two parallel lines) is:
**The first graph** (the one showing a solid line through (0, 4) and (-2, 0) and a dashed line through (-4, 0) and (0, 8)).
This graph correctly represents the two equations as parallel lines:
- The solid line (y = 2x + 4) passes through (0, 4).
- The dashed line (y = 2x + 8) passes through (0, 8).
Thus, the first option is the correct choice.