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A student claims that the equations \(3x-2y=5\) and \(6x-4y=12\) have infinitely many solutions because the ratios of the coefficients of \(x\) and \(y\) are equal. Considering the student's error, which conclusion is correct?एक विद्यार्थी कहता है कि समीकरणों \(3x-2y=5\) और \(6x-4y=12\) के अनंत हल हैं, क्योंकि \(x\) और \(y\) के गुणांकों के अनुपात बराबर हैं। उसकी त्रुटि को ध्यान में रखते हुए सही निष्कर्ष कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The equations have no solutionदोनों समीकरणों का कोई हल नहीं है
\(\frac{3}{6}=\frac{-2}{-4}=\frac12\), but \(\frac{5}{12}\ne\frac12\). Hence, the lines are parallel and have no solution. Exam tip: always compare all three ratios.\(\frac{3}{6}=\frac{-2}{-4}=\frac12\), पर \(\frac{5}{12}\ne\frac12\)। अतः रेखाएँ समानांतर हैं और कोई हल नहीं है। परीक्षा में तीनों अनुपात अवश्य जाँचें।
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