?(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.
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, but they share the same y-intercept, (0,−3). Thus, the system has one solution at (0,−3).
1 answer
To analyze the system of equations given:
Both equations have the same slope of \(-3\) but different y-intercepts (7 and -7).
This means that the lines represented by these equations are parallel. Since parallel lines never intersect, the system has no solutions.
Therefore, 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.
