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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 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 would 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.

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To determine whether the lines represented by the equations \(x + y = 2\) and \(-x + y = 7\) are parallel or intersecting, we can examine the slopes of the lines derived from these equations.

  1. Convert the equations to slope-intercept form \(y = mx + b\):

    • For \(x + y = 2\): \[ y = -x + 2 \] The slope \(m_1 = -1\).

    • For \(-x + y = 7\): \[ y = x + 7 \] The slope \(m_2 = 1\).

  2. Compare the slopes:

    • The slope of the first line is \(-1\).
    • The slope of the second line is \(1\).

Since the slopes of the two lines are different (\(-1\) and \(1\)), this means that the lines are not parallel and will intersect at some point.

From this analysis, the correct statement would be: "The graph of −x+y=7 is incorrect. The lines would intersect." Therefore, the lines should intersect, not be parallel.

So the correct response is: The graph of −x+y=7 is incorrect. The lines would intersect.