Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0ABoth graphs are correct. The lines should be parallel.%0D%0ABoth graphs are correct. The lines should be parallel.%0D%0A%0D%0AThe graph of −x+y=7 is incorrect. The lines should be parallel.%0D%0AThe graph of negative x plus y equals 7 is incorrect. The lines should be parallel.%0D%0A%0D%0AThe graph of x+y=2 is incorrect. The lines should intersect.%0D%0AThe graph of x plus y equals 2 is incorrect. The lines should intersect.%0D%0A%0D%0AThe graph of −x+y=7 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
To determine if the graph shows the system of equations x+y=2 and −x+y=7, we need to analyze the lines represented in the graph.
The correct response is: The graph of −x+y=7 is incorrect. The lines should be parallel.
If the graph showed the system of equations correctly, we would expect the lines representing x+y=2 and −x+y=7 to be parallel. However, since the graph for −x+y=7 is incorrect, it means that the lines do not meet the criteria and are therefore not parallel.
To determine if the graph shows the system of equations x+y=2 and −x+y=7, we can check if the lines represented by the equations are parallel.
To do this, we can compare the slopes of the two lines.
The first equation can be rearranged to y = -x + 2, which has a slope of -1.
The second equation can be rearranged to y = x + 7, which has a slope of 1.
Since the slopes of the two lines are not the same, the lines are not parallel. Therefore, the correct response is: The graph of −x+y=7 is incorrect. The lines should be parallel.