# ravish tells his daughter aarushi,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'.if present ages of aarushi and ravish are x and yyearsrespectively,represent this situation algebraically and graphically.

Given,  present ages of Aarushi and Ravish are x and y years respectively.

Seven years ago,

Age of Aarushi = (x – 7) years

Age of Ravish = (y – 7) years

Age of Ravish = 7 × Age of Aarushi

y – 7 = 7 (x – 7)

⇒ y – 7 = 7x – 49

7xy = 42     ...(1)

Three years hence,

Age of Aarushi = (x + 3) years

Age of Ravish = (y + 3) years

Age of Ravish 3 × Age of Aarushi

y + 3 = 3 (x + 3)

⇒ y + 3 = 3x + 9

3xy = – 6    ...(2)

The given situation can be represented algebraically by the system of simultaneous equation given by 7xy = 42 and 3xy = 6.

Consider the equation

7xy = 42.

y = 7x – 42

When x = 6, y = 7 × 6 – 42 = 42 – 42 = 0

When x = 7, y = 7 × 7 – 42 = 49 – 42 = 7

When x = 5, y = 7 × 5 – 42 = 35 – 42 = – 7

These points can be represented in a table as,

 x 6 7 5 y 0 7 – 7

Consider the equation

3xy = – 6

y = 3x + 6

When x = – 2, y = 3 × (– 2) + 6 = – 6 + 6 = 0

When x = – 1, y =  3 × (– 1) + 6 = – 3 + 6 = 3

When x = 0, y = 3 × 0 + 6 = 0 + 6 = 6

These points can represented in table as,

 x – 2 – 1 0 y 0 3 6

The given situation can be represented graphically as,

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