Qualitative reasoning is an area of study under artificial intelligence. It is used to calculate variables and aspects in real life situations e.g. time, quantity for the purpose of solving and planning using qualitative rather than quantitative variables. Its aim is to come up with reasoning and representation methods that enable people and programs to reason about behavior of people and systems or any variable.

Linear equations, on the other hand, are equations with just plain old variables like *a* rather than something more complicated like *a/c* or square roots. Linear equations are the simplest equations that you will deal with at least every literate person have solved a linear equation. In general, to solve an equation for a given variable, you need to undo whatever has been done to the variables. This is done so as to isolate the variables. This results in “(variables) equals (some number) where (some number) is the answer they are looking for. Suppose I do pushups and play basketball matches, however these two activities depend on one another. Letting *p* represents the number of pushups and *n* represents the number of basketball matches. The number of pushups I do every day depends on the number of basketball matches. If I do 30 pushups every basketball match day, it therefore follows that number of pushups is p = 30b. However, irrespective of basketball match I do 10 pushups every day and in addition I do 25 pushups during basketball match. It, therefore, follows that p = 10 + 25b.

From the first equation the number of pushups is directly depending on the number of basketball matches, that is, p = 30b where *p* represents the number of pushups while *b* represents the number of basketball matches. However, irrespective of a basketball match I always do pushups every day.

This means that although the number of pushups depends on the number of basketball matches, I always do pushups every day. This however should not be confused that the number of pushups does not depend on the number of basketball matches I play, since when I have a basketball match, the number of pushups increases or multiplies.

For example, if I have two matches a day then the number of pushups would be

P=30(2)

=60

## However the number of pushups I do every day is 10. This means that

P=10+25(2)

=60

This shows us that the number of pushups therefore comes to the same irrespective of the formula used to calculate.

In mathematics a system of linear equation (or linear system) is a collection of linear equations involving a set of variables. In this case, we have only two variables *p *and *b*. A solution of linear system or equation is the allocation of numbers to the variables such that all the equations are satisfied at the same time. A solution to the above equation is given by

P = 60

B = 2

The formula (the linear equation) can be used also to calculate the number of pushups during a given period e.g. week or month in a situation whereby I have multiple games during a day. The formula clearly shows the dependence of the number of pushups on the number of matches I have.

In the calculation of linear equations such as this one, the dependence of one factor must come out clearly like in the case above. Although one function is a routine factor it depends heavily on the other.

The variables in this case depend on one another. Linear equations are, therefore, helpful in the calculations of dependent variables, and form an easy method of solving them. Successful application areas of qualitative reasoning include autonomous spacecraft support, failure analysis and on-board diagnosis of vehicles systems, automated generation of control systems or software for photocopiers, conceptual knowledge in ecology and intelligent aids for human learning. In mathematics the theory of linear equations is a branch of linear algebra, a subject which is fundamental to modern mathematics.