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(A) Let $u = \frac{1}{x}$ and $v = \frac{1}{y}$.The equations become:$11v - 7u = 1$  --- $(1)$$9v - 4u = 6$  --- $(2)$To eliminate $u$,multiply $(1)$

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$(\frac{1}{3}, \frac{1}{2})$

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(A) Let $u = \frac{1}{x}$ and $v = \frac{1}{y}$.The equations become:$11v - 7u = 1$  --- $(1)$$9v - 4u = 6$  --- $(2)$To eliminate $u$,multiply $(1)$ by $4$ and $(2)$ by $7$:$44v - 28u = 4$  --- $(3)$$63v - 28u = 42$  --- $(4)$Subtract $(3)$ from $(4)$:$(63v - 44v) = (42 - 4)$$19v = 38 \implies v = 2$Since $v = \frac{1}{y} = 2$,we get $y = \frac{1}{2}$.Substitute $v = 2$ into $(1)$:$11(2) - 7u = 1$$22 - 7u = 1$$7u = 21 \implies u = 3$Since $u = \frac{1}{x} = 3$,we get $x = \frac{1}{3}$.Thus,the solution is $(x, y) = (\frac{1}{3}, \frac{1}{2})$.

Obtain the solution of the following pair of equations by elimination method:
$\frac{11}{y} - \frac{7}{x} = 1, \, \frac{9}{y} - \frac{4}{x} = 6$; $x \neq 0, \, y \neq 0$

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Obtain the solution of the following pair of equations by elimination method:$\frac{11}{y} - \frac{7}{x} = 1, \, \frac{9}{y} - \frac{4}{x} = 6$; $x \neq 0, \, y \neq 0$