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Pair of Linear Equations in Two Variables, Chapter 3, Exercise 3.1, Question 1, Class 10 maths NCERT

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.

Class 10, Mathematics, NCERT, Chapter-3, Pair of Linear Equations in Two Variables, Introduction

A Linear equation may have one, two or more variables with degree (highest power on variables) as one ‘1’ only. Here in this section we are studying “Pair” of linear equations in two variables only, means two equations in two variables with degree ‘one’.
To find out the value of one variable from an equation, only one equation is enough to solve out the value, but in order to find out the value of two variables, at least two linear equations are required. Otherwise we could only find out the value of one variable in terms of another variable which would lead us to infinitely many solutions of the equation.

General forms of a pair of linear equations in two variables:
a1x+b1y+c1=0 --------- (1)
a2x+b2y+c2=0 --------- (2)

There are the following methods to solve the pair of linear equations in two variables:
(i) #Substitution method
(ii) #Elimination method
(iii) #CrossMultiplication method

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