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.

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.
Transcript text: 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.
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Solution

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Solution Steps

Step 1: Identify the equations and their slopes

The given equations are:

  1. \( x + y = 2 \)
  2. \( -x + y = 7 \)
Step 2: Convert equations to slope-intercept form

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

Step 3: Determine the slopes and compare

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

The graph of \( x + y = 2 \) is correct. The graph of \( -x + y = 7 \) is incorrect. The lines should intersect.

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