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. ✅