NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
NCERT Solutions for Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1
Page No: 44
Question 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.
Solution:
Let the present age of Aftab and his daughter be x and y respectively.
Seven years ago,
Age of Aftab = x - 7
Age of his daughter = y - 7
According to the given condition,
Three years hence,
Age of Aftab = x + 3
Age of his daughter = y + 3
According to the given condition,
Thus, the given conditions can be algebraically represented as:
x - 7y = -42
x - 3y = 6
x - 7y = -42 ⇒ × = -42 + 7y
Three solutions of this equation can be written in a table as follows:
× -3y = 6 ⇒ × = 6 + 3y
Three solutions of this equation can be written in a table as follows:
The graphical representation is as follows:
Concept Insight: In order to represent a given situation mathematically, first see what we need to find out in the problem. Here, Aftab and his daughter's present age needs to be found so, so the ages will be represented by variables x and y. The problem talks about their ages seven years ago and three years from now. Here, the words 'seven years ago' means we have to subtract 7 from their present ages, and 'three years from now' or 'three years hence' means we have to add 3 to their present ages. Remember in order to represent the algebraic equations graphically the solution set of equations must be taken as whole numbers only for the accuracy. Graph of the two linear equations will be represented by a straight line.