Which statement is correct by observing the equations (16x+11y=73) and (32x+22y=146)?
Answer and explanation
Correct answer: Both equations represent the same line
The second equation is exactly twice the first: multiplying 16x+11y=73 by 2 gives 32x+22y=146. Hence, both equations represent the same line and the pair has infinitely many common solutions. Equivalently, \(16/32=11/22=73/146=1/2\). Therefore, option B is correct; equal ratios indicate coincident lines, not distinct parallel lines. Exam tip: if \(a_1/a_2=b_1/b_2=c_1/c_2\), the two lines coincide and the pair has infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
Both equations represent the same line
Why is this the correct answer?
The second equation is exactly twice the first: multiplying 16x+11y=73 by 2 gives 32x+22y=146. Hence, both equations represent the same line and the pair has infinitely many common solutions. Equivalently, \(16/32=11/22=73/146=1/2\). Therefore, option B is correct; equal ratios indicate coincident lines, not distinct parallel lines. Exam tip: if \(a_1/a_2=b_1/b_2=c_1/c_2\), the two lines coincide and the pair has infinitely many 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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