10th Class Mathematics Pair of Linear Equations in Two Variables Introduction

      Introduction

In mathematics, a linear equation is a equation in which the degree of the equation is one. Whether it is a linear equation in one variables or two variable or three variables they can be solved and solution can be found. For solving the system of linear equation in three or more variables, the concept of matrix is used which has been developed and introduced for the higher classes. In this chapter we will limit ourself up to the system of linear equation in three variables. The concept of system of linear equation has got wide application in solving the word problems based on day to day life situations.

A linear equation in two variables is a equation which contains a pair of variables which can be graphically represented in xy-plane in the form of coordinate system. By solution of the linear equation we mean to say that the pair of value of the variable that satisfies the given equation. A pair of system of linear equation is the set of two linear in two variables.

In other words, we can say a system of linear equation is nothing but two or more equations that are being solved simultaneously. Mostly, the system of equation can be used by the business people to predict their future events. They will model a real life situation in two system of equations to find the solution and manage their business. We can make an accurate predication by using system of equations. The solution of the system of equations is an ordered pair that satisfies each equation.

A system of linear equation may be consistent or may be inconsistent. If the system of equation is consistent then it will have either unique solution or infinitely many solutions. On the other hand if the system is inconsistent then it will have no solution.