Question

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.

Answer 1

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