# Equations – An Important Component to solve Complex Problems

#### BySteven

Equations play a very vital role in Mathematics. They help in solving many crucial problems that could not be solved otherwise. It is very important to understand the technicalities associated with such problems. With the help of equations, one can easily solve many problems that have a missing element and have proper conditions. Equations can be of different variables. There are different ways of solving systems of equations.

The most simple equation is that of the single system in which only one variable is given and a proper value is provided. They can simply be solved by dividing the respective value by the given quantity of the equation. Then comes the equation of two variables. It can be solved by eliminating one variable by multiplying both equations with a common factor and then carrying out a suitable operation. After eliminating that variable, one can easily calculate the value of one of the variables. After calculating the value of one variable, the value of the second variable is calculated by putting the value of the first variable in any one of the equations. Thus, we can easily compute the value of both those variables. Equations also include more than two variables nowadays. Those equations can be solved by using other methods.

Equations play a very important role in both Mathematics and Physics. Questions of Kinematics, Torque, Thermodynamics, and many important chapters are solved using the concept of equations. Equations are used in Chemistry too. This is the reason why it is very important to know about the different ways to deal with equations. Equations are used to solve problems related to interest, percentage, profit and loss, and many such problems. This article discusses the various ways to solve equations. It will enlighten the readers about the importance of equations too.

## Fundamentals associated with equations:

• Trial and elimination method: In this method, values are added randomly to check whether they satisfy the equation or not. This method cannot be used for the higher degree of equations.

• Simultaneous solution of equations: This method applies to only equations of two variables. In this method, one of the variables is eliminated by multiplying both equations with a common factor. Then the value of a single variable is calculated by dividing the value of the equation by the quantity in front of the respective variable. The value of the other variable is calculated by putting the value of the first variable in the equation. This method is taught to the students in the lower classes and many questions related to this method are asked in crucial examinations.

• Matrices: Using the method of matrices, one can easily solve a system of three variables. One needs to calculate the adjoint of the matrix to obtain the result. This method is used to solve complex problems. This method gives accurate results and is very easy to understand. It is taught to the students in the higher classes. It is important to have the basic ideas of matrices to solve the problems of equations. There are many other methods like the Gauss Jordan Method, the Gauss elimination method, and the Gauss Siedel method. All these methods are used to solve the equations using the concept of Matrices. One can easily solve the problems concerning equations if they have a basic idea of Matrices.