Systems of Linear Equations

Systems of linear equations in n variables: 

Linear equations in two variables: 

General Form: ax+by=0

Example: x+2y = 0 

Linear equations in 3 Variables: 

General Form: ax+by+cz=0

Example: 2x+6y+z=0

A linear equation in n variables x1,x2,X3, ... ,Xn has the form 

a1x1+a2x2+a3x3+. . . +anxn=b . 

The coefficients a1,a2,a3, ... , an are real numbers, and the constant term b is a real number. The number a1 is the coefficient's leading, and x1 is the variable's leading. 

* Linear equations have no products or roots of variables involved in trigonometric, exponential, or logarithmic functions. Variables appear only to the first power. 

Examples of linear equations: 

1) 3x +2 y-z = 0 

2) x +2 y = 4 

3) 7x-3y +2 z = 4 

*In general, there are only 2 types of Systems in Linear Equations. Consistent and Inconsistent Systems.