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

Question

?(1 point)
Responses

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, 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.

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

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 .

Answer 1

To analyze the given system of equations:

1. Equations Given:

   • \(y = -3x + 7\)
   • \(y = -3x - 7\)

2. Slopes:

   • Both equations have a slope of \(-3\).

3. Y-Intercepts:

   • The first equation has a y-intercept at \( (0, 7) \).
   • The second equation has a y-intercept at \( (0, -7) \).

4. Parallel Lines:

   • Since both lines have the same slope but different y-intercepts, the lines are parallel.

5. Conclusion:

   • Lines that are parallel do not intersect at any point, meaning the system has no solutions.

Thus, the best statement that describes the system of equations 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."