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

Question

{
y
=
−
3
x
+
7
y
=
−
3
x
−
7
?(1 point)
Responses

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.
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).

Answer 1

To solve the problem, we will analyze the given equations:

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

Analyzing the slopes and y-intercepts:

• The slope of both equations is \(-3\).
• The y-intercept of the first equation is \(7\) (the point \((0, 7)\)).
• The y-intercept of the second equation is \(-7\) (the point \((0, -7)\)).

Conclusion:

• Since both equations have the same slope of \(-3\) but different y-intercepts (\(7\) and \(-7\)), this means the lines are parallel. Parallel lines never intersect, which indicates that there are no solutions to this system.

Thus, the correct statement that best 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."