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If 3(x − 2) + 2(y + 1) = 31 and 5(x − 2) − 2(y + 1) = 21, what is x + y?यदि 3(x − 2) + 2(y + 1) = 31 और 5(x − 2) − 2(y + 1) = 21, तो x + y का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 53/453/4
Set u = x − 2 and v = y + 1. Adding 3u + 2v = 31 and 5u − 2v = 21 gives 8u = 52, so u = 13/2. Then 2v = 31 − 3(13/2) = 23/2, so v = 23/4. Thus x = u + 2 = 17/2 and y = v − 1 = 19/4, giving x + y = 53/4.मान लें u = x − 2 और v = y + 1। समीकरण 3u + 2v = 31 और 5u − 2v = 21 जोड़ने पर 8u = 52, इसलिए u = 13/2। फिर 2v = 31 − 3(13/2) = 23/2, अतः v = 23/4। इसलिए x = u + 2 = 17/2 और y = v − 1 = 19/4; अतः x + y = 53/4।
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