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

Question

?(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 .

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.
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 given:

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

Both equations have the same slope of \(-3\), but they have different y-intercepts (7 for the first equation and -7 for the second equation). Because they have the same slope but different y-intercepts, the lines are parallel and will never intersect.

Thus, the correct statement from the choices provided 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.