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 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. 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. Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should intersect.
To determine if the given system of equations x+y=2 and −x+y=7 will have parallel lines, we can graph the equations and see if they intersect or are parallel.
To graph the equation x+y=2, we can rearrange it in slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.
For equation x+y=2:
y = -x + 2
Now, we can identify the slope and y-intercept. The slope is -1 and the y-intercept is 2.
For the equation −x+y=7, we can also rearrange it in slope-intercept form y=mx+b:
y = x + 7
Here, the slope is 1 and the y-intercept is 7.
By graphing these equations, we can determine if the lines intersect or are parallel.
If the lines intersect at a single point, the equations have a solution. If the lines are parallel, they will never intersect, indicating that the equations have no solution.
Now, plot the two lines on a graph, and observe if they intersect or are parallel. If the lines intersect at a single point, the answer will be "The graph of −x+y=7 is incorrect. The lines should intersect." If the lines are parallel and do not intersect, the answer will be "Both graphs are correct. The lines should be parallel."