# Linear Equation in two variables

## Definition of Linear Equation in Two Variables

If there are two variables present in an equation having degree 1, then the equation is said to be a linear equation in two variables. The general representation of linear equations in two variables is:

$ax + by + c = 0$

or

$ax + by = - c$

In the above equations, the variables are x and y, and a, b, c are coefficients.

## Solution of a Linear Equation in Two variables

The linear equation which has one variable has a unique solution. However, for the linear equations having two variables, the solution is a pair of values generally written as (x, y). One value is for x and another is for y which satisfies the given equation. Linear equation in two variables has infinitely many solutions.

## Example for the solution of linear equation in two variables

Let a linear equation having two variables is, x + y = 2.

By transferring x to the RHS of the equation, it can be written as,

y = 2 – x

Now let’s put some values of x in the above equation for finding the value of y.

Tabulating the above values:

The above result can also be written in pairs as,

(1, 1), (2, 0), (3, -1), (4, -2)

In the above pairs the first value is for x and the second value is for y.

Now, if we add more values of x in the table, we will get more values of y. This means that the solution of the above equation is never-ending.

Therefore, it may be concluded that, the linear equations having two variables has infinitely many solutions.

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