For infinitely many solutions of (u + 3)x + 8y = 16 and 10x + 20y = 40, what is u?
Answer and explanation
Correct answer: u = 1
Infinitely many solutions occur when the two equations represent the same line. Thus, the ratios of corresponding coefficients and constants must be equal. We have 8/20 = 2/5 and 16/40 = 2/5. Therefore, (u + 3)/10 must also equal 2/5. Solving gives u + 3 = 4, so u = 1. Hence option A is correct. If u had any other listed value, the first coefficient ratio would not match the other ratios, and the equations would not be coincident equations with infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
u = 1
Why is this the correct answer?
Infinitely many solutions occur when the two equations represent the same line. Thus, the ratios of corresponding coefficients and constants must be equal. We have 8/20 = 2/5 and 16/40 = 2/5. Therefore, (u + 3)/10 must also equal 2/5. Solving gives u + 3 = 4, so u = 1. Hence option A is correct. If u had any other listed value, the first coefficient ratio would not match the other ratios, and the equations would not be coincident equations with 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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