knowledge-base/class_9/ch4/0132_algebra.md

metadata

source: ncert_exercises
topic: algebra
class_level: class_9
chapter: ch4
exercise: ex4.2
difficulty: beginner

Class 9 | Ch4: Linear Equations in Two Variables | Exercise 4.2

Q1. Which one of the following options is true and why? y=3x+5 has (i) a unique solution (ii) only two solutions (iii) infinitely many solutions. Answer: (iii) Infinitely many solutions. A linear equation in two variables has infinitely many solutions — for every value of x, there is a corresponding value of y. ✅

Q2. Write four solutions for each of the following: (i) 2x+y=7 (ii) πx+y=9 (iii) x=4y Answer: (i) x=0→y=7: (0,7). x=1→y=5: (1,5). x=2→y=3: (2,3). x=3→y=1: (3,1). ✅ (ii) x=0→y=9: (0,9). x=1→y=9-π: (1,9-π). x=2→y=9-2π: (2,9-2π). x=-1→y=9+π: (-1,9+π). ✅ (iii) y=0→x=0: (0,0). y=1→x=4: (4,1). y=-1→x=-4: (-4,-1). y=2→x=8: (8,2). ✅

Q3. Check which of the following are solutions of 2x+5y=0 and which are not: (i) (0,0) (ii) (1,1) (iii) (-1,1/5) (iv) (4,-3/5) (v) (1/2,1/5) (vi) (1/4,1/5) Answer: (i) 2(0)+5(0)=0=0. YES solution. ✅ (ii) 2(1)+5(1)=7≠0. NOT solution. ✅ (iii) 2(-1)+5(1/5)=-2+1=-1≠0. NOT solution. ✅ (iv) 2(4)+5(-3/5)=8-3=5≠0. NOT solution. ✅ (v) 2(1/2)+5(1/5)=1+1=2≠0. NOT solution. ✅ (vi) 2(1/4)+5(1/5)=1/2+1=3/2≠0. NOT solution. ✅

Q4. Find the value of k if x=2, y=1 is a solution of 2x+3y=k. Answer: Substitute x=2, y=1: 2(2)+3(1)=4+3=7. So k=7. ✅