Linear Equations in Two Variables

An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that ‘a’ and ‘b’ are not both zero, is called a linear equation in two variables.

A linear equation in two variables has infinitely many solutions. The solution of a linear equation is not affected when: a) the same number is added to (or subtracted from) both the sides of the equation. b) both the sides of the equation are multiplied or divided by the same non-zero number. A linear equation in two variables is represented geometrically by a straight line whose points make up the collection of solutions of the equation. This is called the graph of the linear equation. The polynomial equation ax + by + c = 0 is called a linear equation because its geometrical representation is a straight line. To obtain the graph of a linear equation in two variables, it is enough to plot two points corresponding to two solutions and join them by a line. However, it is advisable to plot more than two such points so that you can immediately check the correctness of the graph. The equation of y-axis is x = 0, and the equation of x-axis is y = 0. The graph of x = a is a straight line parallel to the y-axis. The graph of y = a is a straight line parallel to the x-axis. An equation of the type y = mx represents a line passing through the origin. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Moreover, every solution of the linear equation is a point on the graph of the linear equation.

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