Question

If the lines that make up a system of two linear equations are coincident, the system is ____ and the equations are _____options - inconsistent, consistentoptions - dependent, independent

Answer 1

A consistent syste of linear equations is defined as a system wiht at least one solution.

Two linear equations are said to be dependent if one can be obtained by multiplying the other by some number different that zero.

Now, in this case we know that the lines are coincident; this means that they have an infinite number of solutions, therefore the system is consistent.

Since they are the same line (because they coincide) it is clear that we can get one from the other, therefore they are dependent.