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| source: ncert_exercises |
| topic: algebra |
| class_level: class_9 |
| chapter: ch4 |
| exercise: ex4.2 |
| difficulty: beginner |
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| Class 9 | Ch4: Linear Equations in Two Variables | Exercise 4.2 |
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| 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 β for every value of x, there is a corresponding value of y. β
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| Q2. Write four solutions for each of the following: |
| (i) 2x+y=7 (ii) Οx+y=9 (iii) x=4y |
| Answer: |
| (i) x=0βy=7: (0,7). x=1βy=5: (1,5). x=2βy=3: (2,3). x=3βy=1: (3,1). β
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| (ii) x=0βy=9: (0,9). x=1βy=9-Ο: (1,9-Ο). x=2βy=9-2Ο: (2,9-2Ο). x=-1βy=9+Ο: (-1,9+Ο). β
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| (iii) y=0βx=0: (0,0). y=1βx=4: (4,1). y=-1βx=-4: (-4,-1). y=2βx=8: (8,2). β
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| 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. β
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| (ii) 2(1)+5(1)=7β 0. NOT solution. β
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| (iii) 2(-1)+5(1/5)=-2+1=-1β 0. NOT solution. β
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| (iv) 2(4)+5(-3/5)=8-3=5β 0. NOT solution. β
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| (v) 2(1/2)+5(1/5)=1+1=2β 0. NOT solution. β
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| (vi) 2(1/4)+5(1/5)=1/2+1=3/2β 0. NOT solution. β
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| 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. β
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