Question

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.
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Answer 1

Answer:

I am not having graph sorry

Answer 2

$\huge\underline\bold\blue{Question}$

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.

$\huge\underline\bold\blue{Answer}$

Given :

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”.

Solution :

Let the present age of Aftab be 'x'

Let the present age of his daughter 'y'

Now, seven years ago

Aftab's age = x-7

Daughter's age = y-7

According to question

x-7 = 7(y-7)

x-7 = 7y-49

x-7y+42 = 0 .............................(1)

Also three years from now

Aftab's age = x+3

Daughter's age = y+3

According to situation

x+3=3(y+3)

x+3 = 3y+9

x-3y = 6

x-3y-6 = 0 ...............................(2)

Solving equation (1)

$| \frac{x}{y} | \frac{0}{6} | \frac{7}{7} | \frac{14}{8}$

So when x= 0 the equation will be

0-7y+42=0

7y+42=0

7y = 42

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

y = 6

When x = 7, We get

7-7y+42=0

7y+49=0

7y=49

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

y = 7

When x = 14 , we get

14 -7y+42=0

56-7y=0

7y=56

y=$\frac{56}{7}$

y=8

Hence,

When x=0,y=6 i.e.., (0,6)

When x=7,y=7 i.e.., (7,7)

When x=14,y=8 i.e..,(14,8)

Now Solving equation (2)

$| \frac{x}{y} | \frac{36}{10} | \frac{51}{15} | \frac{21}{5}$

So, when x=36 the equation will be

36-3y-6=0

30-3y=0

3y=30

y=$\frac{30}{3}$

y=10

When x=51 , we get

51-3y-6=0

45-3y=0

3y=45

y=$\frac{45}{3}$

y=15

When x=21 , we get

21-3y-6=0

15-3y=0

3y=15

y=$\frac{15}{3}$

y=5

Graph of the given system of equation are above in attachment.