Dependent equations are a set of equations where all the coefficients have a common multiple. This gets eliminated and you are left with a single equation.
Attempting to solve a system of dependent equations will yield no results.
For example: x + y = 8 and 2x + 2y = 16, the common multiple for the terms of the second equation is 2 here.
Dependent equations describe the same line, though they are different. The system formed by dependent equations has an infinite number of solutions.
3x + 4y = 2
6x + 8y = 4
We notice that we get the second equation multiplying by 2 the first equation.
So, both equations are equivalent and all points located on a line, they are located on the other line also.
The system has an infinite number of solutions.