Question

Solve by cross multiplication method: a^2x - b^2y = ab(a+b) , ax-by=2ab

Answer 1

$\huge \mathbb \color{blue}{ANSWER \implies}$

ax/b-by/a=a+b -------------(1)

ax-by=2ab ------------------(2)

Using cross multiplication method we get,

x/(2b²-ab-b²)=y/(-a²-ab+2a²)=1/(a-b)

or, x/(b²-ab)=y/(a²-ab)=1/(a-b)

or, x/(-b)(a-b)=y/a(a-b)=1/(a-b)

Equating the first and the last part,

x/(-b)(a-b)=1/(a-b)

or, x=(-b)(a-b)/(a-b)

or, x=-b

Again equating the last two parts,

y/a(a-b)=1/(a-b)

or, y=a(a-b)/(a-b)

or, y=a

∴, the required solution : x=-b, y=a

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