This 2019 CBSE class 10 Maths 2 mark question is from Linear Equations. An easy 2 mark question in CBSE class 10 sample question paper. A standard NCERT text book question.

Question 12: For what value of p will the following pair of linear equations have infinitely many solutions: (p - 3)x + 3y = p and px + py = 12

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For two equations a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0

Condition for infinitely many solutions => \\frac{a_1}{a_2}) = \\frac{b_1}{b_2}) = \\frac{c_1}{c_2})

The given equations are (p - 3)x + 3y - p = 0 and px + py – 12 = 0

**\\frac{a_1}{a_2}) = \\frac{b_1}{b_2})** ⇒ \\frac{p - 3}{p}) = \\frac{3}{p})

p^{2} – 3p = 3p ⇒ p^{2} – 6p = 0

p(p – 6) = 0 ⇒ p = 0 or 6

**\\frac{b1}{b2}) = \\frac{c1}{c2})** ⇒ \\frac{3}{p}) = \\frac{-p}{-12})

p^{2} = 36 => p = ± 6

The only value that satisfies both the ratios is +6. **The value of p is 6.**

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CBSE Class 10 Maths - 2021

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 2** ▶

2. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 3 to 4** ▶

3. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 5 to 6** ▶

4. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers ▶

5. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 8** | Arithmetic Progressions ▶

6. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 9** | Coordinate Geometry ▶

7. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 10** | Probability ▶

8. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 11** | Probability ▶

9. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 12** | Linear Equations ▶

10. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers & HCF ▶

11. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomials ▶

12. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 15** | Linear Equations ▶

13. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 16** | Coordinate Geometry ▶

14. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 17** | Trigonometric Ratios ▶

15. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 18** | Circles ▶

16. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 19** | Triangles ▶

17. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 20** | Areas Related to Circles ▶

18. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 21** | Statistics - Median ▶

19. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics ▶

20. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations ▶

21. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions ▶

22. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 25** | Triangles ▶

23. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometry ▶

24. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 28** | Statistics ▶

25. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 29** | Surface Areas ▶

26. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 30** | Trigonometry ▶

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