Elementary Algebra

'Elementary' as the name suggests, is the 'basics of algebra'. Beginners start with elementary algebra. If a person has no knowledge beyond that of arithmetic (basic calculation that involves addition, subtraction, multiplication and division), he has to start with Elementary Algebra.

In algebra, we use variables instead of numbers. Variables help in generalizing the concept of problem solving so that in case we have different values, but a similar situation, then simply changing the values of variables will help.

There are many laws that have been derived from years of study and inference that make algebra very easy for calculation. The very basic rule is that the polynomial of highest degree will be placed to the leftmost, and the degree decreases as we move from left to right. The constants (numbers) are to the right hand side (RHS) of the "=" and all the variables at the left hand side (LHS). A system is 'solvable' if there are at least as many equations (or statements) as the number of unknown variables.

To master the art of algebra, one must study the properties of real numbers thoroughly (associative, distributive etc.).

Examples of Linear Equations: 3x + 100 = 250.

Examples of Quadratic Equations: (x+1)(x+2)= 12.

Examples of System of Linear Equations: 3x + y = 25, x - 2y = 5.

Apart from all the positive points in algebra, another is that it also defines "unsolvable problems". If an equation does not have any possible solution, then the system of equations is unsolvable.

Similarly, there can be system of equations that have multiple or infinite solutions. Such systems are classified as "undeterministic"

Systems with more number of variables and lesser number of equations are called "undetermined". Such systems also fall into the category of undeterministic because they're solution cannot be determined, but since its because of lack of information it is placed into a different category of equations.

Similarly, the system of equations with more number of equations than variables is called "overdetermined". In this category, we have repetition of information. Usually there are factors of the same equations repeated.

Now, proceeding with the examples will give you more experience in this field. Remember "there are no short cuts in mathematics, only practice".

Starting algebra from the basics and then moving to the complex variations would be better in case you're a learner and scared of mathematics. After all, we all aim at reducing our problems, don't we?

Happy problem-solving!