Question

Ravish tells his daughter Ayushi 7 years ago I was 7 times as old as you were then also 3 years from now I sell with it and sold as you will be if present age of of Ayushi and Ravi is x and y are respectively represent the situation algebraically and graphically

Answer 1

Heya Mate !!!

Here's Your Answer :-

=> 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

⇒ 7x – y = 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

⇒ 3x – y = – 6    ...(2)

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

Consider the equation

7x – y = 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 ;-

Checkout the 1st Attachment ⤴️

Consider the equation

3x – y = – 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,

Checkout the 2nd Attachment ⤴️

Note :- Please With this Solution , represent them on axis line.

< Hope It Helps >