Final answer:
To determine if a system is dependent, we need to check if the equations representing the system have a unique solution or not. If the equations have a unique solution, the system is independent. If there are infinitely many solutions or no solution, the system is dependent.
Step-by-step explanation:
To determine if a system is dependent, we need to check if the equations representing the system have a unique solution or not. If the equations have a unique solution, the system is independent. If there are infinitely many solutions or no solution, the system is dependent. This can be done by applying the techniques of linear algebra, such as solving the system of equations using methods like substitution, elimination, or matrix operations.
For example, consider the system of equations:
If we try to solve this system, we can see that both equations are equivalent, meaning they represent the same line. Therefore, the system is dependent and has infinitely many solutions.