Question

A linear system is classified as inconsistent. Choose True or False for the statement about the graph of the system.The slopes of the lines are the same.

Answer 1

Answer: true

Explanation:

A system of linear equations can be written as:

y = a*x + c

y = d*x + f

Now, the idea of this is find the point (x, y) where both linear equations meet.

Particularlly, if the slope in both equations is the same, we will have two options:

1) The lines are parallel, so they never met, and the system has no solution.

2) The lines are the same lines (this happens when c = f) and this means that we have infinite solutions.

So it is true, if the slopes are the same, the linear system is not consisten.