Question

What are the three types of systems of linear equations?

Answer 1

The types of systems of linear equations are as follows:

• Dependent: The system has infinitely many solutions. The graphs of the equations represent the same lines. Example: $\left\{\begin{array}{l}2x+2y=4\\ 4x+4y=8\end{array}\right.$. The system has infinitely many solutions.
• Independent: The system has exactly one solution. The graphs of the equations intersect at a single point. Example: $\left\{\begin{array}{l}x+y=5\\ x-y=-1\end{array}\right.$. The only solution to the system is $(2,3)$.
• Inconsistent: The system has no solution. The graphs of the equations are parallel lines. Example: $\left\{\begin{array}{l}x+2y=9\\ 2x+4y=7\end{array}\right.$. The system has no solution.