Questions: Does the graph show the system of equations x+y=2 and -x+y=7? Should the lines for the system be parallel? Both graphs are correct. The lines should be parallel. The graph of x+y=2 is incorrect. The lines should intersect. The graph of -x+y=7 is incorrect. The lines should be parallel. The graph of -x+y=7 is incorrect. The lines should intersect.

Solution Steps

The given equations are:

1. \( x + y = 2 \)
2. \( -x + y = 7 \)

Convert each equation to the form \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.

For \( x + y = 2 \): \[ y = -x + 2 \]

For \( -x + y = 7 \): \[ y = x + 7 \]

The slopes of the equations are:

1. \( y = -x + 2 \) has a slope of \( -1 \)
2. \( y = x + 7 \) has a slope of \( 1 \)

Since the slopes are different (\(-1\) and \(1\)), the lines are not parallel and will intersect.

Final Answer