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.

Let present age of Aftab be x years and present age of his daughter be y years.

Case I. Seven years ago,

Age of Aftab = (x - 7) years

Age of his daughter = (y - 7) years

According to question :

(x - 7) = 7 (y - 7)

⇒ x - 7 = 7y - 49

⇒ x - 7y = -42

Case II.

Three years later,

Age of Aftab = (x + 3) years

Age of his daughter = (y + 3) years

Accoring to questions,

x + 3 = 3 (y + 3)

⇒ x + 3 = 3y + 9

⇒ x — 3y = 6

So, algebraic expression be

x - 7y = -42    ...(i)

x - 3y = 6    ...(ii)

Graphical representation

For eq. (i), we have

x - 7y = -42

⇒    x — 7y — 42

Thus, we have following table :

From eqn. (ii), we have

x -3y = 6

⇒    x = 3y + 6

Thus, we have following table



When we plot the graph of equations. We find that both the lines intersect at the point (42, 12). Therefore, x = 42, y = 12 is the solution of the given system of equations.



Fig. 3.1.