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Linear Equation In Two Variables

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04 Linear Equation In Two Variables

LINEAR EQUATION IN TWO VARIABLES

Linear Equation in two variables:

The equation of the type ax + by = c, 3x+y=5 has two variables x and y. The degree of this equation is 1.

So this is called linear equation in two variables.

General form:

The linear equation in two variables can be represented in general form as

ax + by +c = 0.where a, b ≠ 0.

e.g. 3x + y $–$ 5 = 0.

Solution of linear equation in two variables

The values of x, y which satisfies the equation is called the solution of equation.

e.g. 3x + y $–$ 5

x = 0, y = 5 is the solution of given equation.

x = 1, y = 2 is the solution of given equation.

So, (0, 5) and (1, 2) are the solution of given equation.

Also, (3, -4), (4, -7), (5/3, 0….are the solutions of the given equation.

A linear equation in two variables can have infinitely many solutions.

The graph of linear equation is a straight line.

All points on the straight line satisfy the equation of line.

Conversely,

Every solution of linear equation in two variables is a point on the graph.

Equation of a line:

The equation of $\text{x}$ axis is y = 0

The equation of $\text{y}$ axis is x = 0

The equation of a line parallel to $\text{x}$ axis is y = b

The equation of a line parallel to y axis is x = a.

The equation of a line passing through origin y = mx.