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.

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:

x1234
y10-1-2
Linear Equation in Two Variables

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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