Question
Determine the number of solutions to this system of linear equations:
y=x+5
y=−x+5(1 point)
Responses
2
2
1
1
infinite
infinite
0
0
Skip to navigation
y=x+5
y=−x+5(1 point)
Responses
2
2
1
1
infinite
infinite
0
0
Skip to navigation
Answers
Answer
Use the image to answer the question.
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 equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
Skip to navigation
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 equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
Skip to navigation
Answer
Use the image to answer the question.
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 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?
(1 point)
Responses
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
Skip to navigation
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 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?
(1 point)
Responses
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
Skip to navigation
Answer
Which of these graphs shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions?(1 point)
Responses
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis.
Skip to navigation
Responses
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis.
Skip to navigation
Answered by
GPT 3.5
The system of equations is given by:
y = x + 5
y = -x + 5
To determine the number of solutions, we can compare the slopes of both equations.
In the first equation, the slope is 1 (since the coefficient of x is 1).
In the second equation, the slope is -1 (since the coefficient of x is -1).
Since the slopes are different, the two equations represent two different lines. These lines will intersect at a single point, so there is only 1 solution to the system of equations.
Therefore, the correct answer is:
1
y = x + 5
y = -x + 5
To determine the number of solutions, we can compare the slopes of both equations.
In the first equation, the slope is 1 (since the coefficient of x is 1).
In the second equation, the slope is -1 (since the coefficient of x is -1).
Since the slopes are different, the two equations represent two different lines. These lines will intersect at a single point, so there is only 1 solution to the system of equations.
Therefore, the correct answer is:
1
Answered by
GPT 3.5
The statement is false, because the lines have an intersection point.
The given equations are y = -x + 3 and x + y = 8. By graphing these equations, we can see that the solid line and the dashed line intersect at the point (3, 5). This intersection point indicates that there is a solution to the system of equations, contradicting the statement that there is no solution.
Therefore, the correct answer is:
The statement is false, because the lines have an intersection point.
The given equations are y = -x + 3 and x + y = 8. By graphing these equations, we can see that the solid line and the dashed line intersect at the point (3, 5). This intersection point indicates that there is a solution to the system of equations, contradicting the statement that there is no solution.
Therefore, the correct answer is:
The statement is false, because the lines have an intersection point.
Answered by
GPT 3.5
The graph shows the lines for the system of equations x+y=2 and −x+y=7, and the lines should intersect.
From the given information, we can see that the solid line passes through the points (0, 2) and (2, 0), and the dashed line passes through the points (-7, 0) and (7, 0).
By substituting the coordinates of these points into the equations, we can verify that they satisfy both equations:
For the solid line:
(0) + (2) = 2 (satisfies x+y=2)
(2) + (0) = 2 (satisfies x+y=2)
For the dashed line:
(-0) + (0) = 7 (does not satisfy −x+y=7)
(7) + (0) = 7 (satisfies −x+y=7)
Therefore, the graph does not correctly represent the equation −x+y=7. Instead of being a horizontal line passing through (7, 0), it should be a line with a non-zero slope.
Since the lines do not correctly represent the system of equations and do not satisfy the properties of the given equations, we can conclude that the correct answer is:
The graph of −x+y=7 is incorrect. The lines should intersect.
From the given information, we can see that the solid line passes through the points (0, 2) and (2, 0), and the dashed line passes through the points (-7, 0) and (7, 0).
By substituting the coordinates of these points into the equations, we can verify that they satisfy both equations:
For the solid line:
(0) + (2) = 2 (satisfies x+y=2)
(2) + (0) = 2 (satisfies x+y=2)
For the dashed line:
(-0) + (0) = 7 (does not satisfy −x+y=7)
(7) + (0) = 7 (satisfies −x+y=7)
Therefore, the graph does not correctly represent the equation −x+y=7. Instead of being a horizontal line passing through (7, 0), it should be a line with a non-zero slope.
Since the lines do not correctly represent the system of equations and do not satisfy the properties of the given equations, we can conclude that the correct answer is:
The graph of −x+y=7 is incorrect. The lines should intersect.
Answered by
GPT 3.5
The correct answer is the graph described as:
"A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points (0, 6) and (6, 0)."
In this graph, the line represents the equation y = -x + 6. This line intersects the x-axis and the y-axis, indicating that it has an infinite number of solutions. Additionally, the line 3x + 3y = 18 can be simplified to x + y = 6, which is the same equation as y = -x + 6. Therefore, the two equations represent the same line and have an infinite number of solutions.
Therefore, the correct answer is:
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points (0, 6) and (6, 0).
"A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points (0, 6) and (6, 0)."
In this graph, the line represents the equation y = -x + 6. This line intersects the x-axis and the y-axis, indicating that it has an infinite number of solutions. Additionally, the line 3x + 3y = 18 can be simplified to x + y = 6, which is the same equation as y = -x + 6. Therefore, the two equations represent the same line and have an infinite number of solutions.
Therefore, the correct answer is:
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points (0, 6) and (6, 0).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.