**Linear System of Equations**

A system of equations in which each equation is linear.

For any linear system, exactly one of the following will be true: There is only one solution, there are infinitely many solutions (consistent), or there are no solutions (inconsistent). A linear system with more equations than variables is called overdetermined, and a linear system with more variables than equations is called underdetermined.

**See also**

Coefficient matrix, augmented matrix, Gaussian elimination, Gauss-Jordan elimination

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