Class-9 : Maths - Chapter : 4 Linear Equations In Two Variables (Ex-4.1 Ex-4.2 Ex-4.3 Ex-4.4)

Linear Equations In Two Variables

This chapter will introduce the students to the linear equation in two variables, i.e., ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables.

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To download Chapter 4 (Linear Equations In Two Variables) solutions in PDF for future use please click on the link below.

Ex - 4.1 : Download PDF

Ex - 4.2 : Download PDF

Ex - 4.3 : Download PDF

Ex - 4.4 : Download PDF

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Points To Remember

Linear Equations In Two Variables

An equation of the form ax + by + c = 0 where a, b, c are real numbers and x, y are variables, is 

called a linear equation in two variables.

Here ‘a’ is called coefficient of x, ‘b’ is called coefficients of y and c is called constant term.

Eg. 6x + 2y + 5 = 0, 5x – 2y + 3 = 0 etc.

Solution Of a Linear Equation

Let ax + by + c = 0 be a given linear equation in x and y.

Then, a pair of values, one for x and one for y, which satisfy the given equation, is called its solution.

If x=α and y=β satisfy the equation ax + by + c = 0 then we can say that the ordered pair (α,β) is its solution.

A Linear Equation In Two Variable Has Infinitely Many Solutions

We can get many many solutions in the following way.

Pick a value of your choice for x (say x = 2) in 2x + 3y = 12. Then the equation reduces to 4+3y = 12, which is a linear equation in one variable. On solving this, you get y = 8/3. So (2, 8/3) is another solution of 2x + 3y = 12. Similarly, choosing x = —5, you find that the equation becomes — 10 + 3y = 12. This gives y =22/3. So, (-5, 22/3) is another solution of 2x + 3y = 12. 

So there is no end to different solutions of a linear equation in two variables.

Note : An easy way of getting a solution is to take x = 0 and get the corresponding value of y. 

Similarly, we can put y =0 and obtain the corresponding value of x.

Graph Of a Linear Equation In Two Variables

Method of drawing a graph of ax + by + c = 0, a≠0, b≠0

Step 1 : Express y in terms of x

Step 2 : Choose some convenient values of x and find the corresponding values of y satisfying the given equation.

Step 3 : Write down these values of x and y in the form of a table.

Step 4 : Plot the ordered pairs (x,y) from the table on a graph paper.

Step 5 : Join these points by a straight line and extend it in both the directions.

The line is the graph of the equation ax + by + c = 0.

Equation of lines parallel to x-axis and y-axis

• The equation of x-axis is y=0 and the graph is a line parallel to y-axis.

• The equation of y-axis is x=0 and the graph is a line parallel to x-axis.

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NBSE Solutions for Class 9 Maths for all Chapters by NBSE Guide Online are provided here. Just click on the chapter wise links given below :

• Chapter 1 Number System

• Chapter 2 Polynomials

• Chapter 3 Co-ordinate Geometry

• Chapter 4 Linear Equations In Two Variables

The solution list comprises all the chapter-wise answers to the questions present in the NBSE book for Class 9 in a very precise and lucid manner, maintaining the objective of text books.

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Related Links

NBSE Class 9 Book-keeping & Accountancy

NBSE Class 10 Book-keeping & Accountancy

NBSE Class 10 Mathematics Solutions