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दो चर वाले निम्नलिखित रैखिक समीकरणों के निकाय को हल करें: 2x + 3y + 8 = 0 और x − y − 1 = 0?

Mathematics

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Answer

x=−1x = -1

y=−2y = -2

Step-by-step solution

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दिए गए समीकरण हैं:

  1. 2x+3y+8=02x + 3y + 8 = 0
  2. x−y−1=0x - y - 1 = 0

  1. समीकरण 2 से xx को yy के पदों में व्यक्त करें।

    x−y−1=0x - y - 1 = 0 x=y+1(समीकरण 3)x = y + 1 \quad \text{(समीकरण 3)}

  2. समीकरण 3 से xx के मान को समीकरण 1 में प्रतिस्थापित करें।

    2(y+1)+3y+8=02(y + 1) + 3y + 8 = 0 2y+2+3y+8=02y + 2 + 3y + 8 = 0 5y+10=05y + 10 = 0

  3. yy के लिए हल करें।

    5y=−105y = -10 y=−105y = \frac{-10}{5} y=−2y = -2

  4. yy के मान को समीकरण 3 में प्रतिस्थापित करके xx का मान ज्ञात करें।

    x=y+1x = y + 1 x=−2+1x = -2 + 1 x=−1x = -1

    इसलिए, समीकरणों के निकाय का हल है:
    x=−1x = \boxed{-1}
    y=−2y = \boxed{-2}

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