Question

$\frac{3a}{x} - \frac{2b}{y} = - 5 \\ \frac{a}{x} + \frac{3b}{y} = 2$
please solve equations
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Answer 1

Step-by-step explanation:

The given equations are

$\frac{3a}{x} - \frac{2b}{y} = - 5 \\ \frac{a}{x} + \frac{3b}{y} = 2$

$\tt \purple{ \: Put \: \: \: \frac{1}{x} = u \: \: \: and \: \: \frac{1}{y} = v}$

So, the equations becomes

$(3a)u - (2b)v = - 5 \\ (a)u+ (3b)v= 2$

$\implies(3a)u - (2b)v + 5 = 0 \\ \implies (a)u+ (3b)v - 2 = 0$

Applying cross multiplication method,

$\frac{u}{4b - 15b} = \frac{v}{5a + 6a} = \frac{1}{9ab + 2ab}$

$\implies \frac{u}{ - 11b} = \frac{v}{11a} = \frac{1}{11ab }$

$\implies \pink{ u = \frac{ - 1}{a} \: \: \: and \: \: \: v = \frac{1}{b }}$

So,

$\implies \frac{1}{x} = \frac{ - 1}{a} \: \: \: and \: \: \: \frac{1}{y} = \frac{1}{b }$

$\implies \sf\red{ x = - a \: \: \: and \: \: \: y = b }$