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# 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: 