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Find the value of \(k\) for which the pair \(x+ky=2\) and \(2x+6y=4\) has infinitely many solutions.उस \(k\) का मान ज्ञात कीजिए जिसके लिए \(x+ky=2\) और \(2x+6y=4\) युग्मित समीकरणों के अनंत हल हों।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(k=3\)\(k=3\)
For infinitely many solutions, the equations must be proportional. Compare \(2x\) with \(x\): multiplying \(x+ky=2\) by \(2\) gives \(2x+2ky=4\). To match \(2x+6y=4\), we need \(2k=6\Rightarrow k=3\).अनंत हलों के लिए समीकरण समानुपाती (proportional) होने चाहिए। \(x+ky=2\) को \(2\) से गुणा करने पर \(2x+2ky=4\) मिलता है। इसे \(2x+6y=4\) से मिलाने के लिए \(2k=6\Rightarrow k=3\)।
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