source: ncert_exercises
topic: algebra
class_level: class_10
chapter: ch3
exercise: ex3.4
difficulty: intermediate
Class 10 | Ch3: Pair of Linear Equations | Exercise 3.4 (Elimination Method)
Q1. Solve by elimination: (i) x+y=5, 2x-3y=4 (ii) 3x+4y=10, 2x-2y=2 (iii) 3x-5y-4=0, 9x=2y+7 (iv) x/2+2y/3=-1, x-y/3=3 Answer: (i) Multiply (i) by 3: 3x+3y=15. Add to 2x-3y=4: 5x=19 → x=19/5, y=6/5. ✅ (ii) Multiply (ii) by 2: 4x-4y=4. Add to 3x+4y=10: 7x=14 → x=2, y=1. ✅ (iii) Multiply first by 3: 9x-15y=12. 9x-2y=7. Subtract: 13y=−5 → y=−5/13, x=9/13. ✅ (iv) Multiply x-y/3=3 by 6: 6x-2y=18. x/2+2y/3=-1 → multiply by 6: 3x+4y=-6. Solve: x=2, y=-3. ✅
Q2. Solve: (3x/2)-(5y/3)=-2 and x/3+y/2=13/6. Answer: Multiply both by 6: 9x-10y=-12 and 2x+3y=13. Multiply second by 10/3: not clean. Better: 3×(2x+3y=13): 6x+9y=39. 2×(9x-10y=-12): 18x-20y=-24. Solve: x=1, y=3. Wait — multiply eq1 by 3: 27x-30y=-36. Multiply eq2 by 10: 20x+30y=130. Add: 47x=94 → x=2, y=3. ✅
Q3. Five years ago Nuri was 3 times as old as Sonu. 10 years later Nuri will be twice as old. How old are they? Answer: Let Nuri=x, Sonu=y. x-5=3(y-5) → x-3y=-10. x+10=2(y+10) → x-2y=10. Subtract: y=20, x=50. ✅
Q4. Meena went to bank to withdraw ₹2000 in ₹50 and ₹100 notes. She gets 25 notes total. How many of each? Answer: x+y=25 (notes), 50x+100y=2000 → x+2y=40. Subtract: y=15, x=10. ✅