DESIGN AND IMPLEMENTATION OF COMPUTER SOFTWARE FOR THE SOLUTION OF LINEAR EQUATION

 
ABSTRACT
Life’s circumstances are mathematical in nature. It is therefore clear that answers to such circumstances are obtainable through mathematical processes. Hence this can be achieved if form of mathematical equations and finding the appropriate methods of solving such problem (equation). Linear equation is just an algebraic expression in which certain constants must be summed up, divided or multiplied to find a variable (unknown value) in the expression. Hence designing software for the solution of linear equation makes the system (software) more timely, more accurate and easy to report generation, which makes the system to which they are applied efficient. The primary aim of this study is to develop a software (computerize) for the solution of linear equation.    
 
CHAPTER ONE
INTRODUCTION
The mathematical nature of life circumstances has triggered off the research methodology in mankind, in his usual inquisitive nature to find and adduce various methods and techniques for solving life’s problems. This is achieved by reducing life’s activities to mathematical equation in linear forms to make it possible to handle the numerous variables of life. Before proceeding let’s consider the basic definition of linear equation.
A liners equation is an algebraic equation or expression, which is in the first-degree order i.e. the highest power that it can attain, is to an indent of 1. Linear equation usually take the form A x B  = C, where A, B, C are all constants (known values) and X is the variable (unknown value) to be found. Often a linear equation may contain many variable so that we may have AX1 + AX2 + AX2 -------  + A x N = B, here each a is called the constant and the co-efficient of X, where X = X1, X2 ---- XN, also each X need not be equal to each other. When we have this sort of equation we call it Linear equation for examples:
            (1)        2X  =  3
            (2)        7M  = 8 + 5M
            (3)        4 + 3X  = 17
            (4)        4 – 4X  = 9  - 12X
            (5)        3 (4C –7) –4 (4C – 1)  = 0
Solution for (1) takes the usual form X = 3/2
For (2) we may write m = 4. i.e 7m  - 5m = 8 
2m  = 8, m  = 8/2  = 4
For (3) X  = 41/3  or 4. 333, in this case
3X = 17 – 4, 3  x  = 13
    X  = 13/3  =  41/3
For (4) X  = 5/8, that is to say
4 – 4X + 12X  = 9  - 4
8X  = 5
X  = 5/8  
For (5) C  = 41/4  
3 (4C  - 7) – 4  (4C – 1)  = 0
Remove brackets
12C  - 21 – 16C  + 4  = 0
-4C – 17  = 0
Divide both ides by – 4
C  = 17/4,  =  -  41/4
1.1  STATEMENT OF THE PROBLEM
Solving linear equation may sometimes involve rigorous calculation and approximation of numbers. The use of parenthesis (Brackets), negative signs can make solving linear equation very lengthy and may sometimes be confiding to the human mind at a certain point. Hence this has made the solution so labourious and an uphill task if it must be correctly applied as a solution system. The method of information storage and retrieval process of accumulated figures and substation is not an easy task. If there are no automated system of information storage and retrieval, the application of linear equation is virtually impossible, as much time than required will be spent before an accurate result is generated. Human beings cannot really tackle the ambition and sometimes complex calculations involved in using the system of solution easily which delays the result for its real field application.
1.2   OBJECTIVES OF THE STUDY
The main concern of this project work is to study the methods and processes for solving linear equation. A careful study of the method of solution (Linear equation) and application revealed errors and problems affecting the effectiveness and efficiency of the system are detected and corrective recommendations are made. A new computerized system designed and implemented to take care of the solution system (Linear equation), this made the process involved to be more timely, more accurate and the whole solution system more efficient. The generality of task involved were made easy and interesting as the system now makes early generation of result. 
1.3  SIGNIFICANCE OF THE STUDY
The significance of this study is make the solution technique to solving linear equation (i.e most life is problem) easier and faster and hence reducing time wastage. Also the significance of the study is to help reduce stress on the human brain associated with lots of reasoning when solving linear equation. Also the significance of the study is to help student, teachers who see mathematics as a very difficult subject look more like fun.
1.4   SCOPE OF THE STUDY
Due to some limitation from my side, which includes
(i)         Financial burden
(ii)        Limited knowledge on my own part
 (iii)       Limited time factor
The system will only be able to carryout linear equation with a single term, i.e. the new system will not be able to carryout arithmetical operations involving terms. In order words it cannot add, subtract, divide and multiply like terms. Throughout the study deals on linear equation the new system will not be able to carryout other mathematical operation on other mathematical operators like the greater than (>), less than (<), greater than or equal to (≥) and less than or equal to (≤)
1.5  ASSUMPTION
In order to make head way in this study of solution of linear equation certain conditions must be assumed to be true thus;
(1) It is assumed than life’s circumstances are quantitative
(2) It is assumed that linear equation is accurate, reliable and adequate enough
(3)  It is assumed that the solutions are error free
(4) Assumption is made that all life’s circumstances are relative in nature.
(5) Also an assumption is made that the approximated values adequately represent the life circumstances.