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Which statement is correct for \(2x+5y=1\) and \(3x+7y=4\)?\(2x+5y=1\) और \(3x+7y=4\) के लिए कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: They have exactly one solution.इनके ठीक एक हल है।
Multiply \(2x+5y=1\) by \(3\): \(6x+15y=3\).
Multiply \(3x+7y=4\) by \(2\): \(6x+14y=8\).
Subtract: \((6x+15y)-(6x+14y)=3-8\Rightarrow y=-5\).
Substitute into \(2x+5y=1\): \(2x+5(-5)=1\Rightarrow 2x-25=1\Rightarrow x=13\).
Since we get a definite \((x,y)=(13,-5)\), there is exactly one solution.\(2x+5y=1\) को \(3\) से गुणा करें: \(6x+15y=3\).
\(3x+7y=4\) को \(2\) से गुणा करें: \(6x+14y=8\).
घटाएँ: \((6x+15y)-(6x+14y)=3-8\Rightarrow y=-5\).
अब \(2x+5y=1\) में \(y=-5\) रखें: \(2x+5(-5)=1\Rightarrow 2x-25=1\Rightarrow x=13\).
क्योंकि \((x,y)=(13,-5)\) निश्चित मिलता है, इसलिए ठीक एक हल है।
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