A set of equations for which we get a common solution is known as system of equations. System of equations can be either linear or non-linear.

Two set of equations will have two variables, three set of equations will have three variables and so on. System of equations can have any number of variables which can be linear or non-linear.

A system of equations is a collection of two or more unknowns where we try to find values for each of the unknowns which satisfies every equation in the system. Linear System of Equations

Linear equations use only linear functions and operations. Exponents will not be higher than one. When graphed, it will be a straight line.
Example: x + y + z = 6
They are mostly used in analysis.

Non-Linear System of Equations

It can consist of trignometric functions, multiplication or division by variables. One or more of the variables may contain an exponent larger than one. When graphed it represents some sort of curves.
Example: $x ^{2}$ + $y^{2}$ + z = 4
Non-linear equations dominate the realm of higher math and science.

A general system of m linear equations with n unknowns can be written as

$a_{11}x_{1}$ + $a_{12}x_{2}$ + .........+ $a_{1n}x_{n}$ = $b_{1}$
$a_{21}x_{1}$ + $a_{22}x_{2}$ + .........+ $a_{2n}x_{n}$ = $b_{2}$
...... ........
....... .......
$a_{m1}x_{1}$ + $a_{m2}x_{2}$ + .........+ $a_{mn}x_{n}$ = $b_{m}$