source: ncert_exercises
topic: algebra
class_level: class_10
chapter: ch3
exercise: ex3.1
difficulty: beginner
Class 10 | Ch3: Pair of Linear Equations | Exercise 3.1
Consistency of pair a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0:
- Unique solution (consistent): a₁/a₂ ≠ b₁/b₂ → lines intersect
- Infinite solutions (consistent): a₁/a₂ = b₁/b₂ = c₁/c₂ → coincident lines
- No solution (inconsistent): a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → parallel lines
Q1. Aftab's present age is 7 times his son's. 5 years hence father's age=3 times son's. Represent algebraically. Answer: Let son's age=y, father's age=x. x=7y → x-7y=0. x+5=3(y+5) → x-3y=10. ✅
Q2. Speed of a boat in still water is twice the speed of stream. Form equations. Answer: Let speed of boat=x, speed of stream=y. x=2y → x-2y=0. Time downstream + upstream conditions form second equation. ✅
Q3. Yash scored 40 marks in test of 60 questions (1 mark right, -1/4 mark wrong). Form equations. Answer: Let right answers=x, wrong=y. x+y=60. x-y/4=40 → 4x-y=160. ✅
Q4. A lending library has fixed charge plus charge per day. Saritha paid ₹27 for 3 days, Susy paid ₹21 for 5 days. Form equations. Answer: Let fixed charge=x, per day charge=y. x+3y=27. x+5y=21. ✅