To analyze the system of equations \(x + y = 2\) and \(-x + y = 7\), we can determine whether the lines represented by these equations are parallel or if they intersect.
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Finding the slope and y-intercept of each line:
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For the equation \(x + y = 2\): \[ y = -x + 2 \] Here, the slope (m) is -1, and the y-intercept (b) is 2.
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For the equation \(-x + y = 7\): \[ y = x + 7 \] Here, the slope (m) is 1, and the y-intercept (b) is 7.
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Analyzing the slopes:
- The slope of the first line is -1.
- The slope of the second line is 1.
Since the slopes are different (-1 and 1), the lines are not parallel and will intersect at some point.
Given this analysis, the correct conclusion is that the graph of either of the equations may be incorrect if they are drawn parallel. The pair of equations defines lines that should intersect at a point in the Cartesian plane.
So, the correct answer would be:
The graph of \(x + y = 2\) is incorrect. The lines should intersect.