Question

1/3a+/5b=1/15,1/2a+1/3b=1/12​

Answer 1

$Given \: \frac{1}{3a} + \frac{1}{5b} = \frac{1}{15}$

/* Multiplying each term by 15 , we get */

$\implies \frac{5}{a} + \frac{3}{b} = 1 \: ---(1)$

$Given \: \frac{1}{2a} + \frac{1}{3b} = \frac{1}{12}$

/* Multiplying each term by 12 , we get */

$\implies \frac{6}{a} + \frac{4}{b} = 1 \: ---(2)$

$Let \: \frac{1}{a} = x , \: \frac{1}{b} = y$

$Now, Equations \: becomes, \\5x + 3y = 1 \: --(3)$

$and \: 6x + 4y = 1 \: ---(4)$

$From\: equations \:(3) \: and \:(4) , we \:get$

$\implies 5x + 3y = 6x + 4y$

$\implies 5x - 6x = 4y - 3y$

$\implies -x = y \: ---(5)$

/* Put y = -x in equation (3), we get */

$\implies 5x + 3(-x) = 1$

$\implies 5x - 3x = 1$

$\implies 2x = 1$

$\implies x = \frac{1}{2} \: -- (6)$

/* put value of x in equation (5) , we get */

$\implies -\frac{1}(2} = y \: ---(7)$

Therefore.,

$x = \frac{1}{a}= \frac{1}{2}$

$Value \: of \: a = 2$

$y = \frac{1}{b}= -\frac{1}{2}$

$Value \: of \: b = -2$

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