Algebra/Solutions of systems of linear equations

A solution of a system of linear equations is a set of numbers for each variable that makes every equation true.

Number of solutions for a system of linear equations

A system can either have
1. Zero solutions
2. One solution
3. Infinitely many solutions

This can be demonstrated using 2 variable sets of equations.

No solutions $\begin{matrix} 3 x + 2 y = 12 \\ 3 x + 2 y = 12 \end{matrix}$

One solution $\begin{matrix} x - y = 1 \\ 3 x + y = 9 \end{matrix}$

Infinite solutions $\begin{matrix} x - y = 0 \\ 5 x - 5 y = 0 \end{matrix}$