---
source: ncert_exercises
topic: algebra
class_level: class_9
chapter: ch4
exercise: ex4.1
difficulty: beginner
---

Class 9 | Ch4: Linear Equations in Two Variables | Exercise 4.1

Key concepts:
Linear equation in two variables: ax + by + c = 0 where a,b,c are real numbers and a,b not both zero.
Every linear equation has infinitely many solutions.
Solution = ordered pair (x,y) satisfying the equation.

Q1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Answer: Let cost of pen = ₹x, cost of notebook = ₹y.
Condition: y = 2x → y - 2x = 0 or 2x - y = 0. ✅

Q2. Express the following linear equations in the form ax+by+c=0 and indicate values of a,b,c:
(i) 2x+3y=9.35  (ii) x-y/5-10=0  (iii) -2x+3y=6  (iv) x=3y  (v) 2x=-5y  (vi) 3x+2=0  (vii) y-2=0  (viii) 5=2x
Answer:
(i) 2x+3y-9.35=0. a=2, b=3, c=-9.35. ✅
(ii) x-y/5-10=0. a=1, b=-1/5, c=-10. ✅
(iii) -2x+3y-6=0. a=-2, b=3, c=-6. ✅
(iv) x-3y+0=0. a=1, b=-3, c=0. ✅
(v) 2x+5y+0=0. a=2, b=5, c=0. ✅
(vi) 3x+0y+2=0. a=3, b=0, c=2. ✅
(vii) 0x+y-2=0. a=0, b=1, c=-2. ✅
(viii) -2x+0y+5=0. a=-2, b=0, c=5. ✅