What is the value of (p) for (px+6y=18) and (10x+15y=45) to have infinitely many solutions?
Answer and explanation
Correct answer: 4
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constant terms must be equal: p/10 = 6/15 = 18/45. Since both 6/15 and 18/45 equal 2/5, p/10 = 2/5 gives p = 4. Therefore, option C is correct. Exam tip: For infinitely many solutions, check a₁/a₂ = b₁/b₂ = c₁/c₂. Option 3 is incorrect because 3/10 is not equal to 2/5.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constant terms must be equal: p/10 = 6/15 = 18/45. Since both 6/15 and 18/45 equal 2/5, p/10 = 2/5 gives p = 4. Therefore, option C is correct. Exam tip: For infinitely many solutions, check a₁/a₂ = b₁/b₂ = c₁/c₂. Option 3 is incorrect because 3/10 is not equal to 2/5.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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