This thread is the co-winner of the First prize in the Classroom Lecture Contest.
• Classroom lecture about basics of Maths algebra.

I know Maths is a subject where we need understand the basic, without learning basic we can learn it. Today I will teach you about how to solve an equation

Example 1 :

Let's say we have an equation 4x-3=5

Step 1 take constant 3 to the other side then negative sign of 3 will change as its the rule the sign changes form + to - and vice versa when we take any constant or variable to the other side. So the equation now becomes 4x=3+5=8

Step 2 Now when we take 4 to the other side it becomes denominator and equation becomes x=8/4

And the answer comes out as x=2

Example 2 when we have two equations and have two variable x and y and have to find value of both.

3x+y=5-------1
x-4y=2--------2

In this case we will use substitution method.

Equation 1 can be written as

y=5-3x

Now we have value of y which can be substituted in 2 equation so equation 2 becomes

x-4(5-3x)=2

Now solving this equation it becomes

x-20+12x=2

Taking variable to one side and constants to another side it becomea

x+12x=2+20

So 13x= 22

x=22/13

Putting value of x in 1 or 2 equation we will get the value of y so putting it 2 equation, it becomes

22/13-4y=2

It now becomes

4y=22/13-2

4y= - 4/13

Hence y=( - 4/13)/4

y= - 1/13

Hence x=22/13 & y=-1/13

We can verify the answer by putting these values in any of the equation 1 or 2

If we put values in eq 1

It is 3*22/13+(-1/13) answer should be 5

After solving it we get 66/13-1/13=65/13=5

Hence above are the values of x and y

Hope you all understood how to solve the linear equations in next lecture I will teach about how to solve non linear equations.
• How often we forget how revolutionary algebra in maths was! I still remember how I panicked when I met algebra. Later I got used to it and I can now solve complex calculus.
The stronger a light shines the darker are the shadows around it.

• Even me too. I was not good in maths in childhood but later I was so much passionate about maths that I used to study maths only leaving all other subjects a side. Algebra was never a nightmare for me. I still love to algebra.
Sanjeev

" We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.”
– Abraham Lincoln

• While I was in school, I could never understand Algebra. It was a headache subject to me. However, with sheer luck, I managed to pass the examination with a marginal score. When I saw your thread title "Basics of Algebra", I was damn happy that someone would teach me Algebra online from the scratch. Alas! the confusion continues. I am yet to get your basics of Algebra. You haven't gone into basics of Algebra but beyond the basics.

Anyway, understanding people will surely understand your basics of Algebra.

No life without Sun

• Sun, this is the basic and if you want to learn beyond this then I will have to teach some topics from 5th standard.
Sanjeev

" We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.”
– Abraham Lincoln

• The author has put up a basic Algebra lecture to solve equations to find out unknowns.

Algebra is one of the most fascinating part of Maths and somehow I have a liking for it. As I had Maths till my graduation I used it everywhere to find out solutions whether they are the simple equations or most complicated ones.

This lecture reminds me of that old time when we were using Algebra so much.

Knowledge is power.

• A good lecture on elementary Algebra.

Many students are afraid of Algebra as initially it looks as difficult. With practice it comes under one's grip and then only it's utility is well understood.

Thoughts exchanged is knowledge gained.

• Umesh, yes being an engineering student I also had studied algebra through out my college also. Maths overall is a good subject. I was fascinated towards differential and integral calculus where also basics of algebra is used. Now a days I feel kids fear of maths but I don't why they fear as its a very interesting subject all you need is to understand basics.

Neeru, yes algebra is interesting only thing is you should have the knowledge of basic algebra to solve equations and find the value of variables.

Sanjeev

" We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.”
– Abraham Lincoln

• Algebra is an extension of arithmetic. In arithmetic we simply do the four operations with numbers. In algebra we are generalizing them with alphabets.
e.g: 2+3=5 or 4+6=10 or 35+12=47, etc. But these refer to only those numerical values used in the operation. When we use Algebraic method this simply give the form: a+b=c. That can be called an equation. In this equation two letters are unknown, they can be a, b or c. If two of these unknowns are substituted we get the third one. This algebra is simply an extension of arithmetics.

tmsankaran

• #649969 yes Sankaran its an extension of arithmetic only difference is of variables which are in algebra which we find out by substitution method. Arithmatic is a basic mathematics which deals in finding out the value of numbers by using simple computation and using operations like addition, subtraction, multiplication, division whereas in algebra from these operations we find out the value of variable of an equation.
Sanjeev

" We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.”
– Abraham Lincoln

• It is really good to see the basic equation solving in the forum. You should also try the other method as the 3rd example with both coefficients of x and y has values because in your 2nd example in both the equation, the coefficient of one of the variable is 1 which is easy to solve by substitution method. In this case, you may have to equate one of the variables in both the equations by multiplying each other with cross coefficients and continue solving the equation.
Nice to be in ISC and feel the difference.

• Sarojha, Actually I started with the very basic equations as taking typical examples won't be easy to explain people who don't have basic knowledge of algebra. I will try to take examples of what you told.
Sanjeev

" We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.”
– Abraham Lincoln

• Sanjeev, please note that you must avoid replying to all responses. You may, if required, post a combined reply after two or three responses fall in.
'Real knowledge is to know the extent of one's ignorance' - Confucious.

• OK sir I will keep this in mind. But what is the reason why should it not be done?
Sanjeev

" We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.”
– Abraham Lincoln

• I am a bachelor student and I still find difficulty in solving the questions related to the algebra. I think you have to improve your mathematics skills in the beginning of your learning career. As, things get worse if you will leave the things behind. Thanks!