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CBSE Linear Equations in Two Variables Class 9th Formulas

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Linear equation in one variable:  Linear equation of the form ax + b = 0, where a, b are real numbers such that a≠ 0. For example, 3x + 5 = 0. The letters used in an equation are called variables or unknowns. In the equation 3x + 5 = 0;

x is called the variable of the equation.

Linear equation in two variable:

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. Let us consider the following equations:

(i) 3x + y = 7

(ii) 4x – y = 3

(iii) √2x - √3y = 9

(iv) y = 2x + 5

Note : If in the equation ax+ by = c; we have a = 0 and b≠ 0 or b = 0 and a≠ 0 .Then the equation reduces to by = c or ax = c. In both case we get an equation in one variable. So, it is generally assumed that both a and b are non-zero as given in the above definition.

 Remember: A linear equation in two variables has infinitely many solutions.

• Graph of a linear equation in two variables:

The graph of every linear equation in two variables is a striaght line.

Algorithm:  To draw the graph of a linear equation in one variable we may follow the following steps:

Step I: Obtain the linear equation.

Step II : If the equation is of the form ax = b; a ≠ 0 then plot the point (b/a,0) and one more point (b/a, β) where β is any real number on the graph paper.

If the equation is of the form ay= b, a ≠ 0 then plot the point (0,b/a) and (α,b/a), where α is any real number on the graph paper.

Step III : Join the points plotted in step II to obtain the required line.

•The point (a, 0) where the straight line cross x-axis is called its x-intercept point and ‘a’ is called x-intercept.

•The point (0, b) where the straight line crosses y-axis is called its y-intercept point and ‘b’ is called y-intercept.

• x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.

•The graph x = a is a straight line parallel to the y-axis.

•The graph y = a is a striaght 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.  More over every  solution of the linear equation is a point on the graph of the linear equation. 

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