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 intersect.
The graph of negative x plus y equals 7 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.
The statement "Both graphs are correct. The lines should be parallel." is correct.
are you sure
Apologies for any confusion. You're correct - this was misleading. The two given lines are not parallel. They will intersect because the slopes are not equal (for the first equation, slope is -1, for the second, it is 1). So, the correct response would be something similar to "Both graphs should be correct and the lines should intersect.". The information to accurately determine if the graphs are drawn correctly or not wasn't provided. Please disregard the misleading previous response.
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=7 is incorrect. The lines should be parallel.
The graph of x+y=2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of a system of equations x+y=2 and -x+y=7 should show two intersecting lines, not parallel lines. The correct response would be "The graph of -x+y=7 is incorrect. The lines should intersect." or "The graph of x+y=2 is incorrect. The lines should intersect." depending on which graph is incorrect. Both lines cannot be correct if they are parallel because the given equations are not parallel lines.
The correct response is:
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should intersect.
Therefore, both graphs are incorrect and the lines should intersect, not be parallel.
To determine whether the given system of equations is parallel or not, we need to analyze the graph of the equations.
The first equation, x+y=2, can be rewritten as y=−x+2. This is a linear equation with a negative slope, which means that the line will slant downwards from left to right.
The second equation, −x+y=7, can be rewritten as y=x+7. Similarly, this is a linear equation with a positive slope, so the line will slant upwards from left to right.
Now, let's plot the lines on a graph to see if they intersect or if they are parallel. By combining the two equations and plotting them on a graph, we can visualize the relationship between them.
If we take the y-intercepts of both equations, we can find the point (0,2) for y=−x+2 and the point (0,7) for y=x+7.
By connecting these points with a line, we can see that the lines do not intersect. In fact, they are running parallel to each other.
Therefore, the correct answer is: Both graphs are correct, and the lines should be parallel.