Question

solve for x and y :
${ \frac{ax}{b} - \frac{by}{a} = a + b }$
and
$ax - by = 2ab$
First answer will be marked as brainliest
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Answer 1

★Given,

$\bold{ax/b-by/a=a+b... EQ1}$

$\bold{ax-by=2ab.... EQ2}$

★SOLUTION:

$\bold{By\:cross\: multiplying\: EQ1\: and \:EQ2}$

$\bold{........X...........Y................1}$

$\bold{-b/a......-(a+b)..... a/b.....- b/a}$

$\bold{-b......... -2ab......... a........ - b}$

$\bold{X/-b/a(-2ab)-(-b)(-(a+b))=Y/-(a+b)(a)-(-2ab)(a/b)=1/a/b(-b)-a(-b/a)}$

$\bold{X/2b^2-ab-b^2=Y/-a^2-ab+2a^2=1/-a+b}$

$\bold{X/b^2-ab=Y/a^2-ab=1/-a+b}$

$\bold{X/b(b-a)=Y/a(a-b)=1/-a+b}$

$\bold{X/b(b-a)=Y/-a(b-a)=1/b-a}$

$\bold{X/b=Y/-a=1}$

$\bold{X/b=1, Y/-a=1}$

$\bold{X=b. Y=-a}$

★ANSWER:

➡️$\bold{(X,Y)=(b,-a)}$

Answer 2

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