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.

Ans.Let the present age of Aftab and his daughter be x and y respectively.

So, seven years ago,

Aftab's age = \(x - 7\)

Age of Aftab's daughter = \(y-7\)

According to the given statement in the question:

=>\(x-7 = 7(y-7)\)
=>\(x-7 = 7y-49\)
=>\(x-7y = -42\)............(i)

Three solutions of the equation (i) are :

\(\begin{array} {|r|r|}\hline x & -7 & 0 & 7 \\ \hline y & 5 & 6 & 7 \\ \hline \end{array}\)

Now, three years hence,
Aftab's age = \(x+3\)
Age of Aftab's daughter = \(y+3\)

According to the given statement in the question:

=>\(x + 3 = 3(y+3)\)
=>\(x + 3 = 3y + 9\)
=>\(x -3y = 6\)............(ii)

Three solutions of the equation (ii) are :
\(\begin{array} {|r|r|}\hline x & 6 & 3 & 0 \\ \hline y & 0 & -1 & -2 \\ \hline \end{array}\)
Now the graph for the above equations (i) and (ii) will be: