Ex 3.1, 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.” Represent this situation algebraically & graphically.
Let the Current age of Aftab be x years.
& let Current age of Aftab’s daughter be y years.
Given that
“Seven years ago, I was seven times as old as you were then”
Seven years ago,
Age of Aftab = x − 7
Age of Aftab’s daughter = y − 7
Aftab was seven times as old as Aftab’s daughter
(x – 7) = 7(y – 7)
(x – 7) = 7y – 49
x – 7y = 7 − 49
x – 7y = −42
Also,
“three years from now, I shall be three times as old as you will be “
Three years later,
Age of Aftab = x + 3
Age of Aftab’s daughter = y + 3
Aftab will be three times as Aftab’s daughter
(x + 3) = 3(y + 3)
(x + 3) = 3y + 9
x – 3y = 9 − 3
x – 3y = 6
So, our equations are
x – 7y = −42 ...(1)
x – 3y = 6
For Equation (1)
x – 7y = −42
Let x = 0
0 − 7y = −42
−7y = −42
y = (−42)/(−7)
y = 6
So, x = 0, y = 6 is a solution
i.e. (0, 6) is a solution
Let x = 7
7 − 7y = −42
−7y = −42 − 7
y = (−49)/(−7)
y = 7
So, x = 7, y = 7 is a solution
i.e. (7, 7) is a solution
For Equation (2)
x − 3y = 6
Putting x = 0
0 − 3y = 6
−3y = 6
y = 6/(−3)
y = −2
So, x = 0, y = −2 is a solution
i.e. (0, −2) is a solution
Putting y = 0
x − 3(0) = 6
x – 0 = 6
x = 6
So, x = 6, y = 0 is a solution
i.e. (6, 0) is a solution
We will plot both equations on the graph

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.