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

$a_{11}x_{1}$ + $a_{12}x_{2}$ + .........+ $a_{1n}x_{n}$ = $b_{1}$

$a_{21}x_{1}$ + $a_{22}x_{2}$ + .........+ $a_{2n}x_{n}$ = $b_{2}$

...... ........

....... .......

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