Chapter I : Linear Equations in two variables in two variables

Example – 21. 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 and graphically.

Solution :- Let the present age of Aftab be x and that of his daughter y.

7 years ago, age of Aftab = x - 7 and age of his daughter = y - 7.

According to question,        x - 7 = 7(y - 7)

Or,              x - 7y + 42 = 0   ---   ---   ---   ---   (1)

After 3 years, age of Aftab = x + 3 and age of his daughter = y + 3.

According to question,         x + 3 = 3(y + 3)

Or,               x – 3y – 6 = 0  ---   ---   ---   ---   (2)

The above statement represented algebraically are (1) and (2).

To represent graphically, draw the graph. The points are given below:

For equation (1) :-&

For equation (2) :-