Linear System

A linear system is a set of two or more linear equations involving the same set of variables. The goal is to find the values of the variables that satisfy all equations simultaneously.

Examples

$$\{\begin{array}{l}{x}_1+x_2=2\\ x_1-x_2=0\end{array}$$

This system has 1 unique solution, so it is consistent

$$\{\begin{array}{l}{x}_1+x_2=1\\ x_1+x_2=3\end{array}$$

This system has no solutions. Thus, it refers to an inconsistent system (which refers to a system with no solutions)

$$\{\begin{array}{l}{x}_1+x_2=2\\ 2x_1+2x_2=4\end{array}$$

This system has infinitely many solutions, and is also consistent.