Question

solve: 6x + 3y = 6xy & 2x + 4y = 5xy​

Answer 1

Answer:

6x+3y=6xy

3 (2x+y)=6xy

2x+y=2xy eq.1

2x+4y=5xy eq.2

subtract eq.1 and eq.2

so,

2x+y=2xy

2x+4y=5xy

- - -

-3y= -3xy

x=1

put the value of x in eq.1 or 2

2x+y=2xy

2 (1)+y=2 (1)y

2+y=2y

y=2

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Answer 2

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

$\rm{ \frac{6}{y} + \frac{3}{x} = 6.......(i)}$

$\rm{\frac{2}{y} + \frac{4}{x} = 5........(ii)}$

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${\bold{\underline{\underline{Putting\: \frac{1}{x} =p \: and \: \frac{1}{y}=q \: in \: the \: given \: equation}}}}$

$\rm{3p+6q-6=0}$

$\rm{4p+2q-5=0}$

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

⟾$\rm{ \frac{p}{ - 30 - ( - 12)} = \frac{q}{ - 24 - ( - 15)} = \frac{1}{6 - 24} }$

⟾$\rm{ \frac{p}{ - 18} \frac{ - q}{ - 9} = \frac{1}{ - 18} }$

⟾$\rm{p = 1 \: and \: q = \frac{1}{2} }$

⟾$\rm{p = \frac{1}{x)} = 1 \: and \: q = \frac{1}{y} = \frac{1}{2} }$

⟾$\rm{x=1 \: and \: y = 2}$

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${\rm{\boxed{\boxed{x=1}}}}$

${\rm{\boxed{\boxed{y=1</p><p>2}}}}$

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