To analyze the given system of equations \( y = 2x + 13 \) and \( y = 2x + 1 \):
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Slopes: Both equations have the same slope of 2. This indicates that the lines are parallel.
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Y-Intercepts: The first equation has a y-intercept of 13 (the point (0, 13)), while the second equation has a y-intercept of 1 (the point (0, 1)). Therefore, they do not share the same y-intercept.
Since the equations have the same slope but different y-intercepts, the lines are parallel and will never intersect. This means there are no solutions to the system of equations.
The correct description of the system is:
"Both equations have a slope of 2, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel."
This matches the response:
"Both equations have a slope of 2, but they do not share the same y -intercept. Thus, the system has no solutions because the lines are parallel."