Can a system of Linear Equations have exactly two distinct solutions
Linear systems of equations form the backbone of many mathematical and real-world applications. But how many solutions can such a system have? Broadly, there are only three possibilities for a system of linear equations:
- A unique solution: The system has one precise solution.
- Infinite solutions: The system represents overlapping equations or a family of solutions.
- No solution: The system represents contradictory equations that cannot coexist.
But what if someone claims that a system of linear equations can have exactly two distinct solutions? Let’s explore why this claim is not possible.