Question

1. solve
$\frac{2}{x} - \frac{3}{y} = 15. \: \frac{8}{x} + \frac{5}{y} = 77$
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Answer 1

$\large\underline\blue{\bold{Given \: Question :- }}$

☆Solve the equations :-

$\bf \:\dfrac{2}{x} - \dfrac{3}{y} = 15$

$\bf \:\dfrac{8}{x} + \dfrac{5}{y} = 77$

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$\large\underline\green{\bold{Solution :- }}$

☆ Let us suppose that

$\bf \:\dfrac{2}{x} - \dfrac{3}{y} = 15 \: ⟼ \: (1)$

$\bf \:\dfrac{8}{x} + \dfrac{5}{y} = 77 \: ⟼ \: (2)$

$\bf \:Let \: \dfrac{1}{x} = u \: ⟼(3) \: and \: \dfrac{1 }{y} = v \: ⟼ \: (4)$

☆So, equation (1) and equation (2) can be rewritten as

$\bf \:2u - 3v = 15 \: ⟼ \: (5)$

$\bf \:8u + 5v = 77 \: ⟼ \: (6)$

☆Multiply equation (6) by 1 and (5) by 4 we get

$\bf⟼ \:8u - 12v = 60 \: ⟼ \: (7)$

$\bf ⟼\:8u + 5v = 77 \: ⟼ \: (8)$

☆On substracting equation (7) from (8), we get

$\bf\implies \:17v = 17$

$\bf\implies \:v = 1 \: ⟼ \: (9)$

☆On substituting value of v = 1 in equation (5), we get

$\bf \:  ⟼ 2u - 3 \times 1 = 15$

$\bf \:  ⟼ 2u = 15 + 3 = 18$

$\bf \:  ⟼ u = 9 \: ⟼ \: (10)$

☆On substituting, equation (9) in (3) and (10) in (4), we get

$\bf \:  ⟼ \dfrac{1}{x} = 9 \: and \: \dfrac{1}{y} = 1$

$\bf\implies \:x = \dfrac{1}{9} \: and \: y = 1.$

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$\begin{gathered}\begin{gathered}\bf So \: values \: are \: = \begin{cases} &\bf{x = \dfrac{1}{9} } \\ &\bf{y = 1} \end{cases}\end{gathered}\end{gathered}$

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