What is the most suitable conclusion by observing (6x+7y=41) and (18x+21y=123)?
Answer and explanation
Correct answer: There are infinitely many solutions
The second equation is exactly three times the first: multiplying 6x+7y=41 by 3 gives 18x+21y=123. Thus both equations represent the same line, so the pair has infinitely many solutions. It does not represent two distinct parallel lines, which would give no solution; the lines are also not perpendicular because their slopes are equal. Exam tip: for equations in standard form, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), the pair has infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
There are infinitely many solutions
Why is this the correct answer?
The second equation is exactly three times the first: multiplying 6x+7y=41 by 3 gives 18x+21y=123. Thus both equations represent the same line, so the pair has infinitely many solutions. It does not represent two distinct parallel lines, which would give no solution; the lines are also not perpendicular because their slopes are equal. Exam tip: for equations in standard form, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), 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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