Question

2. 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." Is not the
interesting? Represent this situation algebraically and graphically,
INCERT​

Answer 1

Let Aftab's age right now be x.

Let Aftab's daughter be = y years.

Seven years ago,

Age of Aftab = x - 7

Age of Aftab's daughter = y - 7

Aftab was 7 times as old as Aftab's daughter.

x - 7 = 7(y - 7)

(x - 7) = 7y - 49

x - 7 - 7y + 49 = 0

x - 7y + 42 = 0

Three years later,

Age of Aftab = x + 3

Age of Aftab's daughter = y + 3

Aftab will be three times as Aftab's daughter.

(x + 3) = 3(y + 3)

(x + 3) = 3y + 9

x + 3 - 3y - 9 = 0

x - 3y - 6 = 0

Now, plotting the equation

x - 7y + 42 = 0  (i)

x - 3y -6 = 0      (ii)

Solving (i)

x - 7y + 42 = 0

7y = x + 42

y = $\frac{x+42}{7}$

Let x = 0

y = $\frac{0+42}{7}$

y = $\frac{42}{7}$

y = 6

So, x = 0, y = 6 is a solution, i.e., (0,6) is a solution.

Let x = 7

y = $\frac{7+42}{7}$

y = $\frac{49}{7}$

y = 7

So, x = 7, y = 7 is a solution, i.e., (7,7) is a solution.

Solving (ii)

x - 3y - 6 = 0

3y = x - 6

y = $\frac{x-6}{3}$

Let x = 0

y = $\frac{0-6}{3}$

y = $\frac{-6}{3}$

y = (-2)

So, x = 0, y = -2 is a solution, i.e., (0,-2) is a solution.

Let x = 6

y = $\frac{6-6}{3}$

y = $\frac{0}{3}$

y = 0

So, x = 6, y = 0 is a solution, i.e., (6,0) is a solution.

I have attached the rest of the answer later on......