Question

1/2x+1/3y=2
1/3x+1/2y=13/6
solve it​

Answer 1

$\Large{\underline{\underline{\bf{Solution:-}}}}$

${\sf{let \: \frac{1}{x}=p \: and \: \frac{1}{y} = q \: then \: equations \: change \: as \: follows}}$

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${\sf{\frac{p}{2} + \frac{q}{3} = 2}}$

⟹${\sf{3p + 2q - 12 = 0.........(i)}}$

${\sf{\frac{p}{3} + \frac{q}{2} = \frac{13}{6}}}$

⟹${\sf{2p + 3q - 13 = 0.....(ii)}}$

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${\bold{\underline{\underline{By\: cross\: multiplication\: method:-}}}}$

${\sf{\frac{p}{ - 26 - (36)} = \frac{q}{ - 24 - ( - 39)} = \frac{1}{9 - 4}}}$

⟹${\sf{ \frac{p}{10} = \frac{q}{15} = \frac{1}{5}}}$

⟹${\sf{ \frac{p}{10} = \frac{1}{5} \: and \: \frac{q}{15} = \frac{1}{5}}}$

⟹ ${\sf{p = 2 \: and \: q = 3}}$

⟹${\sf{\frac{1}{x} = 2 \: and \: \frac{1}{y} = 3}}$

⟹${\sf{x = \frac{1}{2} \: and \: y = \frac{1}{3}}}$

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${\sf{\underline{\boxed{\boxed{x=1/2}}}}}$

${\sf{\underline{\boxed{\boxed{y=1/3}}}}}$

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$\Large{\underline{\underline{\bf{Thanks}}}}$