This equation gives following values for x and y
| x | - 35 | - 28 | - 21 | - 14 | - 7 | 0 | 7 | 14 | 21 | 28 | 35 | 42 | 49 |
| y | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
Three years from now:
Aftab’s age `= x + 3` and daughter’s age `= y + 3`
As per question;
`x + 3 = 3(y + 3)`
Or, `x + 3 = 3y + 9`
Or, `x = 3y + 9 – 3`
Or, `x = 3y + 6`
Or, `3y – x + 6 = 0` ……..(2)
This equation gives following values for x and y:
| x | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 |
| y | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
The following graph is plotted for the given pair of linear equations:
Daughter’s age = 12 years and Aftab’s age = 42 years
Question 2: The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Represent this situation algebraically and geometrically.
Solution: Let us assume that price of one bat = x and price of one ball = y. Following equations can be written as per the question:
`3x + 6y = 3900`
Or, `x + 2y = 1300` ……..(1)
This equation will give following values for x and y
| x | 1500 | 1400 | 1300 | 1200 | 1100 |
| y | - 100 | - 50 | 0 | 50 | 100 |
`x + 3y = 1300` ……….(2)
This equation will give following values for x and y
| x | 1600 | 1450 | 1300 | 1150 | 1000 |
| y | - 100 | - 50 | 0 | 50 | 100 |
The following graph is plotted for the given pair of linear equations.
Price of one bat = Rs. 1300 and Price of one ball = zero
Question 3: The cost of 2 kg apples and 1 kg grapes was found to be Rs. 160. After a month, the cost of 4 kg apples and 2 kg grapes is Rs. 300. Represent this situation algebraically and graphically.
Solution: Let us assume that cost of 1 kg apple = x and cost of 1 kg grapes = y. Following equations can be written as per the question.
`2x + y = 160` ……..(1)
This equation gives following values for x and y
| x | 70 | 60 | 50 | 40 |
| y | 20 | 40 | 60 | 80 |
`4x + 2y = 300`
Or, `2x + y = 150` ……..(2)
This equation will give following values for x and y:
| x | 65 | 55 | 45 | 35 |
| y | 20 | 40 | 60 | 80 |
The following graph is plotted for the given pair of linear equations.
Since we get parallel lines so there will be no solution for this pair of linear equations.