what type of system would this be?

y = 5x - 1
y = (1/5)x - 1

linear system

one line intersecting with another line

To determine the type of system, we need to analyze the equations and their relationship to each other.

The given equations are:

y = 5x - 1
y = (1/5)x - 1

Both equations are in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

In this case, we have two different equations, each representing a different line. The slope and y-intercept of the first equation are m = 5 and b = -1, while the slope and y-intercept of the second equation are m = 1/5 and b = -1.

A linear system is said to be consistent if the lines intersect and inconsistent if the lines are parallel and never intersect.

In this case, since the slopes of the lines are not equal (5 and 1/5 are not equal), the lines are not parallel. We conclude that the lines intersect at a single point, causing them to have a unique solution.

Therefore, the given system of equations can be classified as a consistent linear system with a unique solution.