Question
Download Solution PDFसमीकरण 3x + 2y - 6z = 1, 2x - 3y + 3z = -1, x - 4y + z = -6 के निकाय हल है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
समीकरणों 3x + 2y - 6z = 1, 2x - 3y + 3z = -1, x - 4y + z = - 6 के निकाय
अवधारणा:
चरों के उन्मूलन की अवधारणा का प्रयोग कीजिए।
गणना:
समीकरणों का निकाय -
3x + 2y - 6z = 1
2x - 3y + 3z = -1
x - 4y + z = -6
3x + 2y - 6z = 1 के लिए x को अलग करें,
\(\rm x=\frac{1-2y+6z}{3}\)
अब अन्य समीकरणों में प्रतिस्थापित करें,
\(\rm 2\cdot \frac{1-2y+6z}{3}-3y+3z=-1\) और
\(\rm \frac{1-2y+6z}{3}-4y+z=-6\)
सरलीकरण के बाद,
\(\rm \frac{-13y+21z+2}{3}=-1\) और \(\rm \frac{-14y+9z+1}{3}=-6\)
अब, \(\rm \frac{-13y+21z+2}{3}=-1\) के लिए y को अलग करें,
\(\rm y=-\frac{-21z-5}{13}\)
अब अन्य समीकरण में प्रतिस्थापित करें,
\(\frac{-14(-\frac{-21z-5}{13})+9z+1}{3}=-6\) \(\rm \implies -\frac{59z+19}{13}=-6\)
⇒ z = 1
\(\rm y=-\frac{-21z-5}{13}\) के लिए,
z = 1 प्रतिस्थापित करने पर,
\(\rm y=-\frac{-21\cdot1-5}{13}\) ⇒ y = 2
\(\rm x=\frac{1-2y+6z}{3}\) के लिए,
z = 1, y = 2 प्रतिस्थापित करने पर,
\(\rm x=\frac{1-2\cdot2+6\cdot1}{3}\) ⇒ x = 1
समीकरणों के निकाय का हल हैं:
x = 1, y = 2, z = 1
अतः विकल्प (4) सही है।
Last updated on May 26, 2025
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