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
⇒ 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,
| x | 6 | 7 | 5 |
| y | 0 | 7 | – 7 |
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,
| x | – 2 | – 1 | 0 |
| y | 0 | 3 | 6 |
The given situation can be represented graphically as,
