Question

2(3u-v)=5uv and 2(u+3v)=5uv by elimination method

Answer 1

hope it helps..........................

Answer 2

$Given \: 2(3u-v) = 5uv$

$\implies 6u - 2v = 5uv$

/* Dividing both sides by uv, we get */

$\implies \frac{6u}{uv} - \frac{2v}{uv} = \frac{5uv}{uv}$

$\implies \frac{6}{v} - \frac{2}{u} = 5\: --(1)$

$Given \: 2(u+3v) = 5uv$

$\implies 2u + 6v = 5uv$

/* Dividing both sides by uv, we get */

$\implies \frac{2u}{uv} + \frac{6v}{uv} = \frac{5uv}{uv}$

$\implies \frac{2}{v} + \frac{6}{u} = 5\: --(2)$

$Let \: \frac{1}{v} = a \: and \:\frac{1}{u} = b$

$Rewrite \: the \: equations \:(1) \:and \:(2) ,we \:get$

$6a - 2b = 5 \: ---(3)$

$2a + 6b = 5 \: ---(4)$

$Now, 3\times (3) + (4) , we \:get$

$18a - 6b + 2a + 6b = 15 + 5$

$\implies 20a = 20$

$\implies a = 1$

/* Put a = 1 in equation (4), we get */

$2\times 1 + 6b = 5$

$\implies 2 + 6b = 5$

$\implies 6b = 5 - 2$

$\implies 6b = 3$

$\implies b = \frac{3}{6}$

$\implies b = \frac{1}{2}$

$a = 1 = \frac{1}{v} \implies v = 1$

$and \: b = \frac{1}{2} = \frac{1}{u} \implies u = 2$

Therefore.,

$\green { u = 2 \: and \: v = 2}$

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