Class 10 Maths NCERT Complete Solutions Chapter wise
Chapter 1. Real Numbers Solutions
Chapter 2. Polynomials Solutions
Chapter 3. Pair of Linear Equations in Two Variables Solutions
Chapter 4. Quadratic Equations Solutions
Chapter 5. Arithmetic Progression Solutions
Chapter 6. Triangles Solutions
Chapter 7. Coordinate Geometry Solutions
Chapter 8. Introduction to Trigonometry Solutions
Chapter 9. Some Applications of Trigonometry Solutions
Chapter 10. Circles Solutions
Chapter 11. Area Related to Circles Solutions
Chapter 12. Surface Areas and Volumes Solutions
Chapter 13. Statistics Solutions
Chapter 14. Probability Solutions
Pair of Linear Equations in Two Variables Ex 3.1
Pair of Linear Equations in Two Variables Ex 3.2
Pair of Linear Equations in Two Variables Ex 3.3
NCERT Class 10 Maths Ch.3 Pair of Linear Equations in Two Variables Ex 3.1
Q1. Form the pair of linear equations in the following problems, and find their solutions graphically:
(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4more than the number of boys, find the number of boys and girls who took part in the quiz.
Solution:
(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.
Answer:
Q2:
Solution:
Q3:
Solution:
Exercise 3.2 (Solutions of PAIR OF LINEAR EQUATIONS IN TWO VARIABLES)
Exercise 3.2 focuses on solving pairs of linear equations using the elimination method. In this method, we multiply one or both equations by suitable numbers so that one variable gets cancelled when the equations are added or subtracted. Once one variable is eliminated, the remaining equation becomes simple to solve. After finding the value of one variable, we substitute it back into any original equation to get the second value. This exercise helps students understand how to systematically reduce equations and find unique solutions, or identify cases where equations have no solution or infinitely many solutions.
Exercise 3.3 ( Solution of PAIR OF LINEAR EQUATIONS IN TWO VARIABLES)
Exercise 3.3 explains how to solve a pair of linear equations graphically. Each equation is plotted as a straight line on the coordinate plane, and the solution to the pair is found by observing how the two lines behave. If the lines intersect at a single point, the pair has a unique solution. If the lines are parallel, the equations have no solution, and if the lines overlap completely, they have infinitely many solutions. This exercise helps students understand the geometric meaning of solutions and how algebraic equations relate to graphs.
Pair of Linear Equations in Two Variables Ex 3.1