# CBSE Notes for Class 9 Maths Chapter 4 Linear Equations In Two Variables

## Class 9 Maths Chapter 4 Linear Equations In Two Variables

Linear equations introduced in chapter 4 of class 9 are the basics of algebra which you will study in later classes. Linear Equations in Two Variables is all about finding the value of two unknown variables when two Linear Equations are given. GharPeShiksha gives you a strategy to follow, which will help you to score well in this chapter. At GharPeShiksha, we provide students with the best Revision Notes, NCERT solutions, NCERT Exemplar Solutions, Previous Year Questions of this Chapter, Formulae Sheet, Model Answer Sheets designed by our expert teachers. The study material is updated each year as per the syllabus requirements. The sample papers made available by GharPeShiksha are strictly in concurrence with the latest exam paper pattern published by CBSE and other state boards. It is an exclusive feature that the students can enjoy at GharPeShiksha only.

DEFINITION:
When an equation has two variables both of degree one, then that equation is known as linear equation in two variables.
Standard form= ax+by+c=0. (where a, b & c are constants and a,b are not equal to 0.
NOTE: The solution can be found by assuming the value of one of the variable and then proceed to find the other solution.
There are infinitely many solutions for a single linear equation in two variables.
The pair which satisfies the equation is the solution of that particular equation.

## Slope Intercept form

Generally, the linear equation in two variables is written in the slope-intercept form as this is the easiest way to find the slope of the straight line while drawing the graph of it.
The slope-intercept form is
y=mx + c
Here, m represents the slope of the line.

To find the solution of a Linear Equation

1.There is only one solution in the linear equation in one variable but there are infinitely many solutions in the linear equation in two variables.

2.As there are two variables, the solution will be in the form of an ordered pair, i.e. (x, y).

3.The pair which satisfies the equation is the solution of that particular equation.

GRAPHICAL REPRESENTATION OF THE LINEAR EQUATION
For example, Draw the graph of the equation 3x + 4y = 12.
We need to find the solutions of the equation first-
Let x = 0
3(0) + 4y = 12
y = 3
Let y = 0
3x + 4(0) = 12
x = 4
Now draw a table to write the solutions.

Now we can draw the graph easily by plotting these points on the Cartesian plane.

NOTE:

Lines passing through the origin
1. Certain linear equations exist such that their solution is (0, 0). Such equations when represented graphically pass through the origin.
2.The coordinate axes namely x-axis and y-axis can be represented as y=0 and x=0, respectively.
3.Equations of the form y=mx passes through the origin.2

Lines parallel to coordinate axes

1.Linear equations of the form y=a, when represented graphically are lines parallel to the x-axis and a is the y-coordinate of the points in that line.
Example- y=3

Linear equations of the form x=a, when represented graphically are lines parallel to the y-axis and a is the x-coordinate of the points in that line.
X= 4

How to represent linear equation of one variable in two variables?
Example x=3 (in one variable)
Sol: 1.
x + 0.y=3 (in two variable)

2y=5 (in one variable)
0.x + 2.y=5 (in two variable)

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