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**Linear Equation in Two Variables**

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**Introduction to Linear Equation in Two Variables**

An equation in the form of 'ax + by + c = 0' is called a linear equation in two variables 'x' and 'y' where a, b and c are real numbers and a and b are not both zeros. Here a and b are called the coefficients of x and y respectively and c is called the constant term.

The solution of a linear equation is an ordered pair of real numbers which satisfies the equation. The solution is always written as an ordered pair.

Any linear equation in two variables has infinitely many solutions.

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**Graphical Representation of Linear Equations in Two Variables**

A linear equation in two variables represents a straight line geometrically. The straight line is called the graph of the linear equation in two variables.

The solutions of a linear equation can be obtained by substituting different values for x in the equation to find the corresponding values of y.

The values of x and y are represented as an order pair. To plot the graph of a linear equation, its solutions are found algebraically and then the points are plotted on the graph.

Any linear equation of the form 'ax + by + c = 0' represents a straight line on the graph. The points of the straight line make up the collection of solutions of the equation.

Every point that satisfies the linear equation lies on the line. Every point that lies on the line is a solution of the linear equation. A point that does not lie on the line is not a solution of the linear equation.

An equation in the form of y = mx where m is a real number, represents a straight line passing through the origin in a cartesian plane.

The equation of x-axis is y = 0. Equation of any line parallel to x-axis is of the form y = k.

The equation of y-axis is x = 0. Equation of any line parallel to y-axis is of the form x = k.

The solution of a linear equation is not affected when:

(i) the same number is added to (or subtracted from) both the side of an equation.

(ii) multiplying or dividing both the sides of the equation by the same non-zero number.

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