## Introduction:

A **SYSTEM OF LINEAR EQUATIONS** in mathematics is the collection of two or more equations having same variables.in these equation number of variables may change two or more. This system of equation is providing bases for mathematical algebra, they are commonly used in our daily life to provide solution for daily problems here we have example equations.

x + y=5, x plus y, equals, 5

and

2x – y=12,2x minus y, equals, 1

In these two equation “x”,” y” are two variables whose value can change. If we change value of one variable it may affect the other variable. Both are **Linear equations** with two variables. When considered together, they form a **System of Linear** **equations**.

**Application **And Uses Of Linear System Of Equations

Linear system of equations that Are all true together. You must find an answer or answers that works for all the equations at the same time. E.g. if you are working with two LINEAR EQUATION SYSTEM, even though there may be a solution that makes one of equation true, you must find the solution that makes both equation true. LINEAR SYSTEM OF EQUATION can be used to solve everyday problems especially those that are more different to think through without writing anything down.

**Rate Distance and Time**

You can calculate the best routs for your running by creating mathematical expression that takes into account the distance, speed and time for the root we can use same formula to calculate running times can be used to determine speed distance and time duration when travelling by car, plane or train.

Linear system of equation can be used to determine the best loan choice to make when buying a car or a house.

LINEAR SYSTEM OF EQUATION can be used when considering the relationship between the prices of commodity people want to buy at a certain price.

An air traffic controller can use LINEAR SYSTEM OF EQUATION to ensure to airplanes don’t intersect at the same time.

You can use LINEAR SYSTEM OF EQUATION to decide or your best investment option taking into account the duration of the investment the interest it will occur as well as other variables that will affect the end result.

## Methods For Solving Simultaneous Linear Equation.

These methods are given below. we will learn about subsitution method

- Elimination of a Variable
- Substitution
- Cross Multiplication

Evaluation of proportional value of variable

This is a method of solving LINEAR SYSTEM EQUATIONS by removing all but in one of the variables in one of the equations and then solving that equation. This is achieved by isolating the other variable in an equation and then substituting values of these variables in other another equation for example to solve the system of equation x + y =4 and 2x-3y =3 isolate the variable x in the first equation to get

###### then substitutes this value of x into second equation to get

###### by simplifies

x = 4 – y

2(4 – y) – 3y = 3

8 – 2y – 3y =3

-5y = -5

###### put value of y in equation 1 to get value of x.

y =1

X+y=4

X+1=4

X=3

This is a simple way to solve equations, here we can conclude that value of one varaible is linked with another variable. These two equations linked with each other through these variables.

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