# System of Equations and Different Methods to Solve Them

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In a layman’s language, a system of equations can be defined as a limited set of equations whose solutions need to be found. Let us take a few examples to understand the system of equations more clearly. 24x + 53y = 21, 31x + 67y = 2, 47x + 27y = 3, etc are some of the examples of the system of equations.

We have numerous applications of the system of equations in our everyday life. We can have different types of solutions for the system of equations. A system of equations can have no solution at all, have infinitely many solutions, or have a unique solution. In this article, we will discuss the various methods in which the system of equations can be solved along with learning the applications of this concept in our everyday lives.

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## Various Methods for Solving the System of Equations

We have many methods through which we can arrive at the solutions of a pair of systems of equations. An equation that consists of only a single variable can be solved easily, without the need for any specific method.

For a system of equations that has two or three variables, we have some specific methods through which we can find out their solutions. Let us now discuss the various methods through which solutions of the system of equations of two variables can be found.

• Elimination Method: This method is one of the easiest to find out the solutions of a system of equations. In this method, we eliminate one of the variables of the equations using the process of multiplication. The variable that needs to be eliminated is multiplied with such numbers that render the coefficients of the variable the same so that it can be easily subtracted and we are left with only one variable.
• Substitution Method: As the name suggests, in this method we substitute one of the variables with another. Once the substitution process is carried out, we arrive at an equation that remains with only one variable, whose solution can easily be obtained. Once we obtain the solution of one of the variables, we can put that value in the former equation and derive the solution of the other variable.
• Graphical Method: In this method, we use graphs to derive the solutions. At least two values of both the variables need to be found out that satisfy the given equations. When we do this for both the equations, we will get four points that can be plotted on the graph chart. The point at which both the equations intersect with each other is the solution of the pair of equations.

### Applications of System of Equations

We have many real-life applications of the system of equations. In linear programming problems, we use the concept of the system of equations extensively. Even in the concept of linear inequalities, systems of equations are used to derive the required answer.