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Solve ax/b -by/a= a+b,ax-by=2ab |
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Answer» {tex}\\frac { a x } { b } - \\frac { b y } { a } = a + b{/tex}{tex}\\Rightarrow{/tex}\xa0{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\xa0- 2ab^2{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}x(a^2\xa0- 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 geta(b) - by = 2ab{tex}\\Rightarrow{/tex}\xa0-by = ab{tex}\\Rightarrow{/tex}\xa0y = -aSo, x = b and y = -a 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 geta2x−abx=a2b+ab2−2ab2⇒ x(a2−ab)=a2b−ab2⇒x=ab(a−b)a(a−b)⇒x=bSubstituting x = b in (ii), we geta(b) - by = 2ab⇒ -by = ab⇒ y = -aSo, x = b and y = -a |
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