What is the value of d for infinitely many solutions of 4x + dy = 7 and 12x + 15y = 21?
Answer and explanation
Correct answer: d = 5
For infinitely many solutions, the two linear equations must represent the same line. Hence the ratios of corresponding coefficients must be equal: 4/12 = d/15 = 7/21. Both 4/12 and 7/21 simplify to 1/3. Therefore, d/15 = 1/3, giving d = 5. Substitution verifies the result: 4/12 = 5/15 = 7/21 = 1/3. Thus option C is correct. The other options make the y-coefficient ratio different, so the equations would not be coincident and could not have infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
d = 5
Why is this the correct answer?
For infinitely many solutions, the two linear equations must represent the same line. Hence the ratios of corresponding coefficients must be equal: 4/12 = d/15 = 7/21. Both 4/12 and 7/21 simplify to 1/3. Therefore, d/15 = 1/3, giving d = 5. Substitution verifies the result: 4/12 = 5/15 = 7/21 = 1/3. Thus option C is correct. The other options make the y-coefficient ratio different, so the equations would not be coincident and could not have infinitely many common solutions.
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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