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Which statement best describes the system of equations {y=−3x+7y=−3x−7

?(1 point)
Responses

The equations have different slopes and different y-intercepts. Thus, the system has one solution at (−3,7).
The equations have different slopes and different y -intercepts. Thus, the system has one solution at left parenthesis negative 3 comma 7 right parenthesis .

Both equations have a slope of −3, and they share the same y-intercept. Thus, the system has an infinite number of solutions because they are identical lines.
Both equations have a slope of negative 3 , and they share the same y -intercept. Thus, the system has an infinite number of solutions because they are identical lines.

The equations have different slopes, but they share the same y-intercept, (0,−3). Thus, the system has one solution at (0,−3).
The equations have different slopes, but they share the same y -intercept, left parenthesis 0 comma negative 3 right parenthesis . Thus, the system has one solution at left parenthesis 0 comma negative 3 right parenthesis .

Both equations have a slope of −3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.

1 answer

To analyze the system of equations given:

  1. \( y = -3x + 7 \)
  2. \( y = -3x - 7 \)

We can see that both equations have the same slope (-3), which indicates that the lines are parallel. However, they have different y-intercepts (7 for the first equation and -7 for the second equation).

Since parallel lines never intersect, this system of equations has no solutions.

Based on this analysis, the correct statement is:

"Both equations have a slope of -3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel."