Find the value of x and y

Mathematics

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Answer

x=2419,y=1338x = \frac{24}{19}, y = \frac{13}{38}

Step-by-step solution

4 steps

यहाँ xx और yy के मान ज्ञात करने के लिए समीकरणों का हल दिया गया है:

  1. दिए गए समीकरणों को लिखें।

    समीकरण 1: 3x+5y=5.53x + 5y = 5.5
    समीकरण 2: 2x−3y=1.52x - 3y = 1.5

  2. yy पद को समाप्त करने के लिए समीकरणों को गुणा करें।

    समीकरण 1 को 3 से गुणा करें:

    3(3x+5y)=3(5.5)3(3x + 5y) = 3(5.5) 9x+15y=16.5(समीकरण 3)9x + 15y = 16.5 \quad (\text{समीकरण 3})

    समीकरण 2 को 5 से गुणा करें:

    5(2x−3y)=5(1.5)5(2x - 3y) = 5(1.5) 10x−15y=7.5(समीकरण 4)10x - 15y = 7.5 \quad (\text{समीकरण 4})

  3. xx का मान ज्ञात करने के लिए समीकरण 3 और समीकरण 4 को जोड़ें।

    (9x+15y)+(10x−15y)=16.5+7.5(9x + 15y) + (10x - 15y) = 16.5 + 7.5 19x=2419x = 24 x=2419x = \frac{24}{19}

  4. xx के मान को समीकरण 1 में प्रतिस्थापित करके yy का मान ज्ञात करें।

    3(2419)+5y=5.53\left(\frac{24}{19}\right) + 5y = 5.5 7219+5y=5.5\frac{72}{19} + 5y = 5.5 5y=5.5−72195y = 5.5 - \frac{72}{19} 5y=112−72195y = \frac{11}{2} - \frac{72}{19} 5y=11×19−72×22×195y = \frac{11 \times 19 - 72 \times 2}{2 \times 19} 5y=209−144385y = \frac{209 - 144}{38} 5y=65385y = \frac{65}{38} y=6538×5y = \frac{65}{38 \times 5} y=1338y = \frac{13}{38}

    The final answer is x=2419,y=1338x = \frac{24}{19}, y = \frac{13}{38}.

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