## Mathematics Portfolio

August 29, 2011

PATTERNS WITHIN SYSTEM OF LINEAR EQUATION

A system of linear equation is basically dealt with in the algebra unit. It is a collection of the linear equations involving variables of the same set in the in the equations that are involved. For example a 2×2 system of linear equations includes:

x + 2y=10

3x + 4y=15

Here in both the cases the equations only involve two variables that is x and y and no other variable is included.

In the example of a 33 system of linear equations it mostly includes the variables x, y and z for example;

2x + y-z =11

x- 2y + 2z =-2

3x-y+2z =5

Where only the three variables are involved

There are also various properties of the patterns of the linear systems. We will start with the consistency property. If the systems of the equations have common solutions, then they are said to be consistent. This therefore means that graphically the lines should be straight lines. The independence property is also termed as the linear independence. The systems of equations are usually independent since to start with, they are derived algebraically from others. For example the system 3x+4y =9 and 6x +8y =18.

There are different ways of solving the systems of linear equations that includes;

• The elimination of variables
• The substitution of variables technique
• The row reduction method
• The crammers’ rule…
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