Solve question by the method of substitution.
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.

Explanation

Assume the present age of Aftab be `(x)`years and his daughter be `(y)`years.

Present age of Aftab = `(x) `years and his daughter = `(y
)`years
Therefore, `7` years ago, age of Aftab = `(x - 7)` years and his daughter = `(y - 7)` years
Using this information and applying the known condition that `7` years ago, Aftab was `7` times as old as his daughter then:

`x - 7 = 7(y - 7)`
`x - 7 = 7y - 49`
`x - 7y - 7 + 49 = 0`
`x - 7y + 42 = 0`

After `3` years from now, age of Aftab = `(x + 3)` years and his daughter's age = `(y + 3)` years
Also, Aftab will be `3 `times as old as his daughter which can be represented as:
`x + 3 = 3 (y + 3)`

`x + 3 = 3y + 9`
`x - 3y + 3 - 9 = 0`
`x - 3y - 6 = 0`
Thus we have,
`x - 7y + 42 = 0 `--(1)
`x - 3y - 6 = 0` --(2)
Therefore, the algebraic representation is for equation (1) is:
`x - 7y + 42 = 0`
`-7y = - x - 42`
`7y = x + 42`
`y = (x + 42)/7`
And, algebraic representation for equation (2) is:
`x - 3y - 6 = 0`

`- 3y = - x + 6`
`3y = x - 6`
`y = (x - 6)/3`