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Linear Equations In Two Variables

You have solved linear equation with one variable. Now it’s  time to learn how to solve the equation with two variables.

Consider the equations below:

x + 2y + 4 = 0   ,    3x + 4y = 18   ,      5u – 6v = 11 

Here you see that there are two variable, i.e. x and y , whose values are unknown. In earlier post I have given one equation, i.e. ax – b = 0 , similarly here is one equation ax + by + c = 0 where a ≠ 0 , b ≠ 0. 

Now we will learn how to solve these equation given above:

Let us take this equation  3x + 4y = 18 , to solve this equation you have to use trial and error method. When you do trial and error you get x = 2 and  y = 3 . If you do more trial and error method you get many solutions of this, one is that I have give first and another is x = 6 and y = 0 . This shows that linear equations in two variable can have infinite number of solutions. 



Algebra is a branch of mathematics in which we use variable for unknown quantity.

Ex:  1)  ax = b or ax – b = 0

2) 3x – 9 = 3

when we solve these equation we get : 1) x = b/a  and in 2) x = 4 . This means the value of in both these equations are different and can have any value, it is not fixed.

You may have thought that from where this word ‘Algebra‘ came. This word came from the book  Kitab al-muhtasar fi Hisab Aljaber w’al muqabalah  written by Mohammed ibn Musa abu Abdullah al Khowarizmi of Baghdad around 825 A.D., but much before this , Aryabhatta  and Brahmagupta had already done a lot of work in this field.


Commercial Maths

As I have told you maths is used in many place even in banks and this maths is known as Commerce or Commercial Maths. If you had taken loan then you had noticed that they give you a time periods of 1, 1.5 or 3 years. If you had taken loan of 50,000 for 3 years at the rate of 15% p.a. then the simple interest would be as follows:

S.I. = (50,000 * 15 * 3) / 100

= Rs. 22,500

So, till now you have understood that the formula is S.I. = ( P * R * T ) / 100

Another method is that to find the amount and then subtracting it with the principal, this gives you Compound interest.

Ex: On the same information given above the compound will be:

( Remember the time interval changes when the rate is compounded half yearly and annually.) 

Amount = Principal * ( 1 + 15/100 ) * ( 1 + 15/100 ) * ( 1 + 15/100 )

A = 50,000 * ( 1 + 15/100 ) * ( 1 + 15/100 ) * ( 1 + 15/100 )

Therefore,    A = 76043.75

C.I = A – P

= 76,043.75 – 50,000

= Rs. 26,043.75

This shows that C.I. and S.I. different when calculated. If the time span is same then the Interests would be same.


What is Maths? Why some children fear from it? Is it interesting?

Yeah we have answer to this. Maths as all of us know that it is subject where we learn algebra, geometry etc.  If we think on another side it is fun and on other it  is useful. Maths in our daily life affects us in many ways which we often does not  recognize it. Ex: In banks, Maths is mostly used, it is used for calculating interests, loans, income…………………..and many more things. Some children fear from it because  they see maths as a monster or any bad sort of thing.

On other hand we get many benefits of maths, we get loans and interest and we are able to pay it off. If there is no maths than we are not able to pay it and the cycle of loans  go on forever. And when we go for buying bike then the rate of bike depends upon the quality of parts and the quality of engine.

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