What is the most suitable conclusion by observing the equations (6x+7y=41) and (18x+21y=123)?
Answer and explanation
Correct answer: There are infinitely many solutions
Dividing every term of the second equation by 3 gives \(6x+7y=41\), which is exactly the first equation. Hence, both equations represent the same line and have infinitely many common solutions. Therefore, option C is correct. Option B would apply if the two lines were distinct parallel lines. For exams, remember: 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?
Dividing every term of the second equation by 3 gives \(6x+7y=41\), which is exactly the first equation. Hence, both equations represent the same line and have infinitely many common solutions. Therefore, option C is correct. Option B would apply if the two lines were distinct parallel lines. For exams, remember: 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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