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