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Does the graph show the system of equations x + y = 2 and -x + y = 7? Should the lines for the system be parallel?

answers:

The graph of -x + y = 7 is incorrect. The lines should be parallel

The graph of x + y = 2 is incorrect. The lines should intersect.

Both graphs are correct. The lines should be parallel

The graph of -x + y = 7 is incorrect. The lines should intersect

3 answers

To determine whether the lines represented by the equations \( x + y = 2 \) and \( -x + y = 7 \) are parallel or intersecting, we first need to analyze the slopes of each line.

  1. Equation: \( x + y = 2 \)

    • Rearranged: \( y = -x + 2 \)
    • Slope: -1

  2. Equation: \( -x + y = 7 \)

    • Rearranged: \( y = x + 7 \)
    • Slope: 1

Since the slopes of the two lines are different (-1 and 1), the lines are not parallel and will intersect at some point.

Therefore, the correct choice based on these analyses is:

The graph of -x + y = 7 is incorrect. The lines should intersect.

you sure

Yes, I am sure. Let's break it down step-by-step again for clarity:

  1. Equation 1: \( x + y = 2 \)

    • Rearranging to slope-intercept form (y = mx + b): \[ y = -x + 2 \]
    • Here, the slope \( m_1 = -1 \).

  2. Equation 2: \(-x + y = 7\)

    • Rearranging to slope-intercept form: \[ y = x + 7 \]
    • Here, the slope \( m_2 = 1 \).

Comparison of Slopes:

  • The first line has a slope of -1, and the second line has a slope of 1.
  • Since the slopes are different (one is negative and the other is positive), the lines are not parallel and will intersect at some point.

Thus, I confirm that the statement is correct: The graph of -x + y = 7 is incorrect. The lines should intersect.