does the graph show the system of equations X Plus y equals 2 and "-1x" + y equals 7 should the lines for the system be parallel

Answer 1

To determine if the lines represented by the equations \(x + y = 2\) and \(-x + y = 7\) are parallel, we need to compare their slopes.

1. Rewrite the equations in slope-intercept form (y = mx + b):

   • For the first equation \(x + y = 2\): \[ y = -x + 2 \] Here, the slope (m) is \(-1\).

   • For the second equation \(-x + y = 7\): \[ y = x + 7 \] Here, the slope (m) is \(1\).

2. Compare 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. Instead, they will intersect at a point.

In summary, the lines represented by the equations \(x + y = 2\) and \(-x + y = 7\) are not parallel.