Romila went to a stationery shop and purchased 2 erasers and 3 A4 sheets for ₹9. Her friend Sonali saw the new variety of erasers and A4 sheets Romila bought, and she also bought 4 erasers and 6 A4 sheets of the same kind for ₹18. Represent this situation graphically.
Step-by-step solution
Idea: Sonali bought exactly twice what Romila bought and paid exactly twice as much, so her equation is just Romila’s multiplied by 2.
- Let one eraser cost ₹x and one A4 sheet ₹y. Romila: 2x + 3y = 9. Sonali: 4x + 6y = 18.1 mark
- Points on 2x + 3y = 9: (0, 3), (3, 1), (4.5, 0). The same points satisfy 4x + 6y = 18 (e.g. 0 + 18 = 18, 12 + 6 = 18, 18 + 0 = 18).1 mark
- So both equations are represented by one and the same straight line. The ratios agree: 24 = 36 = −9−18 = 12: infinitely many solutions, and the prices cannot be found from this information alone.1 mark
Check: (1.5, 2) is on the line: 3 + 6 = 9 ✓ and 6 + 12 = 18 ✓. So eraser ₹1.50 with sheet ₹2 is possible, and so is eraser ₹3 with sheet ₹1.
Answer to write in the exam
Let eraser = ₹x, A4 sheet = ₹y
2x + 3y = 9 and 4x + 6y = 18
Points: (0, 3), (3, 1), (4.5, 0) satisfy both
24 = 36 = 918 = 12
∴ The lines coincide; infinitely many solutions
Common mistakes that cost marks
- Trying to solve and expecting a single price for each item.
- Drawing two separate lines because the equations look different.
How this can come in the exam
Arun buys 3 pens and 2 pencils for ₹16. His sister buys 6 pens and 4 pencils of the same kind for ₹32.
(i) Write the equations. (ii) Compare the ratios. (iii) What do the graphs look like? (iv) Can you find the price of a pen?
Show answer
(i) 3x + 2y = 16, 6x + 4y = 32 (1 mark). (ii) 36 = 24 = 1632 = 12 (1 mark). (iii) Coincident lines (1 mark). (iv) No, infinitely many solutions, e.g. (4, 2) or (2, 5) (1 mark).Try one yourself
Represent graphically: 1 bun and 2 biscuits cost ₹10; 3 buns and 6 biscuits cost ₹30.
Show answer
x + 2y = 10 and 3x + 6y = 30: the same line through (0, 5) and (10, 0); infinitely many solutions.
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