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Solve ax/b -by/a= a+b,ax-by=2ab

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Solve ax/b -by/a= a+b,ax-by=2ab

Posted by Vanshika Mohit 6 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Sia ? 6 years, 6 months ago

{tex}\frac { a x } { b } - \frac { b y } { a } = a + b{/tex}
{tex}\Rightarrow{/tex} {tex}a^2x - b^2y = a^2b + ab^2{/tex}............(i)
{tex}ax - by = 2ab{/tex}..............................(ii)
Multiply (ii) by -b, we get
{tex}-abx + b^2y = -2ab^2{/tex}.......................(iii)
Adding (i) and (iii), we get
{tex}a^2x - abx = a^2b + ab^2 - 2ab^2{/tex}
{tex}\Rightarrow{/tex} {tex}x(a^2 - ab) = a^2b - ab^2{/tex}
^{{tex}\Rightarrow x = \frac { a b ( a - b ) } { a ( a - b ) }{/tex}

{tex}\Rightarrow x = b{/tex}}
Substituting x = b in (ii), we get
a(b) - by = 2ab
{tex}\Rightarrow{/tex} -by = ab
{tex}\Rightarrow{/tex} y = -a
So, x = b and y = -a

Vandan Dev Barnwal 4 years, 6 months ago

axb−bya=a+b ⇒ a2x−b2y=a2b+ab2............(i) ax−by=2ab..............................(ii) Multiply (ii) by -b, we get −abx+b2y=−2ab2.......................(iii) Adding (i) and (iii), we get a2x−abx=a2b+ab2−2ab2 ⇒ x(a2−ab)=a2b−ab2 ⇒x=ab(a−b)a(a−b) ⇒x=b Substituting x = b in (ii), we get a(b) - by = 2ab ⇒ -by = ab ⇒ y = -a So, x = b and y = -a

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