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 .

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, 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.

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.

Answer 1

To analyze the system of equations:

1. First equation: \( y = -3x + 7 \)
2. Second equation: \( y = -3x - 7 \)

Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

• The slope of both equations \( m = -3 \) is the same.
• The y-intercept for the first equation is \( b = 7 \), and for the second equation, it is \( b = -7 \).

Since both equations have the same slope but different y-intercepts, they are parallel lines. Parallel lines do not intersect, meaning the system of equations has no solutions.

Thus, 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."