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## 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*.

For, x = 1, y = 2 - x = 2 - 1 = 1 | For, x = 2, y = 2 - x = 2 - 2 = 0 | For, x = 3, y = 2 - x = 2 - 3 = - 1 | For, x = 4, y = 2 - x = 2 - 4 = - 2 |

Tabulating the above values:

x | 1 | 2 | 3 | 4 |

y | 1 | 0 | -1 | -2 |

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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