 # System of Equations – The Equations We Study in Mathematics

We probably have studied equations in Mathematics in classes 8 or 9. Those equations can be simultaneous equations or the equation system which consists of a finite set of equations. Where we were required to find out a common solution. We will study the same concept here. Our motive is to make a detailed understanding of the system of equations. How it works, and its importance in our real life.

The system of equations finds its application to find an unknown value in our day-to-day lives which can be presented in the form of variables.

## Define the System of Equations

In the study of Algebra. The system of equations consists of two or more equations. Where solutions are required to be found and this satisfies the same set of variables.

## An Example of the System Of Equations

A system of equations is such which comprises two or more mathematical equations which seek the same solution. Following are examples of the system of equations:

• 3x + y = 12
• 5x – 2y = 56

## What Are the Different Types of Solutions to System of Equations?

When we say ‘let us solve the mathematical equation” we mean we are going to find out an unknown variable by solving the equation. We estimate the unknown values by balancing the equation on both sides. By solving the solution, and finding out the value of the unknown variable we prove that the equation holds true of the equation. The types are as follows:

1. Unique Solutions
2. No Solution
3. Infinitely many Solution

## Explanation of the Types of System of Equations

Let us now understand the types of systems of equations –

#### Unique Solution of a System of Equations:

This system of Equation means that there is only one single solution of the system which means that there is only one value of the variable. You can put it this way the point of intersection of those lines that represent the equation become equal (LHS and RHS become equal). Take for example, 5x = 10, this have a unique solution – x = 2. For this, the LHS will be equal to RHS. So, we say that the linear equations in two variables have a unique solution that satisfies the equations in the system.

#### No Solution:

A system of equations will have no solution if there exists no point where the lines are intersecting each other or that the lines in the graph paper are parallel to each other.

#### Infinite Many Solution:

An equation system can have infinitely many solutions, this happens when there exists a solution set of infinite points on the graph paper. In the graph paper, the lines are seen overlapping each other.

## Methods of Solving System of Equations

Solving any system of equations can consist of many different methods. If we are required to find three variables then we need at least three equations, while to find out equations with four variables, we need 4 equations likewise. Well, there are different methods of solving the system of equations, they are as follows:

1. Substitution Method
2. Elimination Method
3. Graphical Method

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Like, in this content we have precisely discussed the system of equations its motive behind the concept, and the methods of solving the equations. If you are interested to know more about this topic or about any other maths topics enrol in Cuemath classes by visiting their website.