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प्रश्न
Aarush bought 2 pencils and 3 chocolates for ₹ 11 and Tanish bought 1 pencil and 2 chocolates for ₹ 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
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उत्तर
Let the price of a pencil be x and the price of a chocolate be y.
∴ ATQ for Arush = 2x + 3y = 11
ATQ for Tanish = x + 2y = 7
For 2x + 3y = 11
| x | 1 | 4 | 7 |
| y | 3 | 1 | –1 |
For x = 1,
2x + 3y = 11
2(1) + 3y = 11
2 + 3y = 11
3y = 11 – 2
3y = 9
`y = 9/3`
y = 3
For x = 4,
2x + 3y = 11
2(4) + 3y = 11
8 + 3y = 11
3y = 11 – 8
3y = 3
`y = 3/3`
y = 1
For x = 7,
2x + 3y = 11
2(7) + 3y = 11
14 + 3y = 11
3y = 11 – 14
3y = –3
y = –1
For x + 2y = 7
| x | 3 | 1 | 5 |
| y | 2 | 3 | 1 |
For x = 3,
x + 2y = 7
3 + 2y = 7
2y = 7 – 3
2y = 4
`y = 4/2`
y = 2
For x = 1,
x + 2y = 7
1 + 2y = 7
2y = 7 – 1
2y = 6
`y = 6/2`
y = 3
For x = 5,
x + 2y = 7
5 + 2y = 7
2y = 7 – 5
2y = 2
y = 1
