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In the first-quadrant solution region for \(3x+y\le15\) and \(x+3y\le15\), what is the intersection of the two boundary lines?असमानता \(3x+y\le15\) और \(x+3y\le15\) के पहले चतुर्थांश हल क्षेत्र में रेखाओं का प्रतिच्छेद क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \( \left(\frac{15}{4},\frac{15}{4}\right) \)\( \left(\frac{15}{4},\frac{15}{4}\right) \)
Adding the equations gives \(4x+4y=30\), and by symmetry \(x=y=\frac{15}{4}\). Use symmetry when boundary lines have a similar structure.दोनों समीकरण जोड़ने पर \(4x+4y=30\) और सममिति से \(x=y=\frac{15}{4}\) है। समान संरचना वाली रेखाओं में सममिति का उपयोग करें।
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