What is m for infinitely many solutions of 4x + (m − 5)y = 9 and 12x + 6y = 27?
Answer and explanation
Correct answer: m = 7
For infinitely many solutions, both equations must represent the same straight line. Therefore, the ratios of corresponding coefficients must be equal: 4/12 = 9/27 = 1/3. The coefficient of y must follow the same ratio, so (m − 5)/6 = 1/3. Multiplying by 6 gives m − 5 = 2, and hence m = 7. Thus option C is correct. The other options make the y-coefficient ratio different from 1/3, so the three ratios are not equal. In that case the equations do not describe coincident lines and cannot possess infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
m = 7
Why is this the correct answer?
For infinitely many solutions, both equations must represent the same straight line. Therefore, the ratios of corresponding coefficients must be equal: 4/12 = 9/27 = 1/3. The coefficient of y must follow the same ratio, so (m − 5)/6 = 1/3. Multiplying by 6 gives m − 5 = 2, and hence m = 7. Thus option C is correct. The other options make the y-coefficient ratio different from 1/3, so the three ratios are not equal. In that case the equations do not describe coincident lines and cannot possess 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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