NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4
NCERT Solutions for class 10 maths ex 3.4 Pair of Linear Equations in two variables is discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. This ex 3.4 class 10 deals with the graphical and algebraic representations of linear equations in two variables and their different type of solutions such as a unique solution, no solutions or infinitely many solutions, using the five methods namely the Graphical method, substitution method, cross Multiplication method, elimination method and determinant method.
NCERT Solutions for Exercise 3.4 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables These class 10 maths ex 3.4 solutions are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Pair of Linear Equations in Two Variables Class 10 Chapter 3 Excrcise: 3.4
Q1(i) Solve the following pair of linear equations by the elimination method and the substitution method :
Answer:
Elimination Method:
Given, equations
Now, multiplying (1) by 3 we, get
Now, Adding (2) and (3), we get
Substituting this value in (1) we, get
Hence,
Substitution method :
Given, equations
Now, from (1) we have,
substituting this value in (2)
Substituting this value of x in (3)
Hence,
Q1(ii) Solve the following pair of linear equations by the elimination method and the substitution method :
Answer:
Elimination Method:
Given, equations
Now, multiplying (2) by 2 we, get
Now, Adding (1) and (3), we get
Putting this value in (2) we, get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
substituting this value in (1)
Substituting this value of x in (3)
Hence,
Q1(iii} Solve the following pair of linear equations by the elimination method and the substitution method: (iii)
Answer:
Elimination Method:
Given, equations
Now, multiplying (1) by 3 we, get
Now, Subtracting (3) from (2), we get
Putting this value in (1) we, get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
substituting this value in (1)
Substituting this value of x in (3)
Hence,
Q1(iv) Solve the following pair of linear equations by the elimination method and the substitution method :(iv)
Answer:
Elimination Method:
Given, equations
Now, multiplying (2) by 2 we, get
Now, Adding (1) and (3), we get
Putting this value in (2) we, get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
substituting this value in (1)
Substituting this value of x in (3)
Hence,
More About NCERT Solutions for Class 10 Maths Exercise 3.4
In the elimination method from NCERT solutions for Class 10 Maths exercise 3.4 we pick a variable which we need to eliminate then we multiply both the equations with non-zero constants such that the coefficient of the variable we picked becomes numerically equal but with opposite signs (one negative the other positive) so that they get cancelled when we add the equation.
Thus, we are left with the other variable which we can solve easily and get the value of the remaining variable. Once we get the value of the other variable, we substitute it to any of the equations to get the value of the first variable.
In this example, we will eliminate ‘y’ from the equation
x + 2y = 4 ..........(1)
2x - y = 3 ............(2)
We multiply equation (I) with 1 and equation (II) with 2 to make the coefficient of ‘y’ numerically equal.
x + 2y = 4 ..........(3)
4x - 2y = 6 ............(4)
Now add these two equations we get.
5x = 10
x = 10/2 = 2
Now substituting the value of ‘x’ on equation (I) we get.
(2) + 2y = 4
2y = 2
y = 1
So, we have ‘x’ as 2 and ‘y’ as 1.
The elimination method can only be applied if the ratios of the coefficient are different. It doesn’t solve the equations if the ratios are the same.
In the above example, the ratio of equation (I) is 1:2 and the ratio of Equation (II) is 2: -1 which is different. Also students can get access of Pair of linear equations in two variables notes to revise all the concepts discussed in this chapter.
Benefits of NCERT Solutions for Class 10 Maths Exercise 3.4
- Class 10 Maths chapter 3 exercise 3.4 introduces us to a more convenient, easier and time-efficient method for solving a pair of linear equations by elimination method.
- The elimination from NCERT solutions for Class 10 Maths exercise 3.4 method is quite conceptual and this method makes dealing with higher-level questions easier.
- Apart from solving through the algebraic method and graphical method the elimination method of Class 10 Maths chapter 3 exercise 3.4 is quite an easier and time-efficient method to solve the pair of linear equations.
- In some exams, the question asks only the value of one variable so by using the elimination method of Class 10th Maths chapter 3 exercise 3.4 we can eliminate the second variable and end up with the value of the first (required) variable only.
Also see-
NCERT Solutions of Class 10 Subject Wise
Subject Wise NCERT Exemplar Solutions