If (6x+11y=9) and (12x-11y=63), what is the value of (x-y)?यदि (6x+11y=9) और (12x-11y=63), तो (x-y) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{59}{11}\)\(\frac{59}{11}\)
Adding the two equations eliminates \(y\): \(18x=72\), so \(x=4\). Substituting into \(6x+11y=9\) gives \(24+11y=9\), hence \(y=-\frac{15}{11}\). Therefore, \(x-y=4-\left(-\frac{15}{11}\right)=\frac{59}{11}\). \(\frac{15}{11}\) is only the magnitude of \(y\), not the value of \(x-y\). Exam tip: add equations directly when a variable has opposite coefficients.दोनों समीकरणों को जोड़ने पर \(18x=72\) मिलता है, अतः \(x=4\)। अब \(6x+11y=9\) में \(x=4\) रखने पर \(24+11y=9\), इसलिए \(y=-\frac{15}{11}\)। अतः \(x-y=4-\left(-\frac{15}{11}\right)=\frac{59}{11}\)। \(\frac{15}{11}\) केवल \(y\) का परिमाण है, \(x-y\) नहीं। परीक्षा टिप: विपरीत गुणांक वाले पदों को जोड़कर चर को शीघ्र समाप्त करें।
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