NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.3 are designed to help students with their Class 10 exam preparation. These solutions are prepared by subject experts to ensure a deep understanding of solving pairs of linear equations through algebraic methods—specifically substitution and elimination.
Exercise 3.3 focuses on solving linear equations in two variables using both substitution and elimination methods. These methods allow students to manipulate equations to find the values of the variables. Understanding these methods is crucial for students to solve complex algebraic problems with confidence.
NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.3
Q.
Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of Class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen.
Q.
Solve the following system of linear equations 7x – 2y = 5 and 8x + 7y = 15 and verify your answer.
[CBSE - 2024]
NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.3
The solutions are written in a step-by-step manner, strictly adhering to the NCERT guidelines to ensure conceptual clarity and exam-readiness for students.
Q1: Form the pair of linear equations in the following problems, and find their solutions graphically:
-
10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
-
5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pencil and that of one pen.
Solution:
-
Let the number of boys be x and the number of girls be x + 4 (as the number of girls is 4 more than the number of boys).
-
The total number of students is given as 10, so the equation becomes:
x + (x + 4) = 10
Solving the equation:
2x + 4 = 10
2x = 6
x = 3
So, the number of boys is 3 and the number of girls is 3 + 4 = 7.
For the second problem:
-
Let the cost of one pencil be p and the cost of one pen be q.
-
The two given equations are:
5p + 7q = 50
7p + 5q = 46
-
Solve these equations simultaneously to find the values of p and q.
Q2: Solve the following system of linear equations and verify your answer:
7x – 2y = 5
8x + 7y = 15
Solution:
-
We will solve the system using either substitution or elimination method. Let’s use substitution:
From the first equation, solve for x:
7x = 2y + 5
x = (2y + 5)/7
-
Substitute the value of x in the second equation:
8((2y + 5)/7) + 7y = 15
Simplifying and solving the equation will give you the values of x and y.
FAQs: Class 10 Maths Chapter 3 – Exercise 3.3
Q1. What methods are used in Exercise 3.3?
Answer:
Exercise 3.3 uses two algebraic methods to solve linear equations:
-
Substitution Method
-
Elimination Method
Both methods help in finding the values of variables by eliminating one variable at a time.
Q2. How do I use the substitution method?
Answer:
In the substitution method, solve one equation for one variable, then substitute that expression into the second equation. This will give you a single equation with only one variable, which you can solve to find the value of that variable.
Q3. What is the elimination method?
Answer:
In the elimination method, manipulate the two equations to eliminate one of the variables. You can add or subtract the equations to cancel out one variable, making it easier to solve for the remaining variable.
Q4. Which method is better: substitution or elimination?
Answer:
Both methods are useful:
Q5. How do NCERT Solutions help in exam preparation?
Answer:
These solutions provide clear, step-by-step explanations of both methods, helping students practice effectively. By solving these problems, students can improve their algebraic skills and build confidence for exams.