If frac{3}{x}-frac{2}{y}=5 and frac{4}{x}-fra | vedclass

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(B) Let $u = \frac{1}{x}$ and $v = \frac{1}{y}$.The given equations become:$3u - 2v = 5$  --- $(1)$$4u - 5v = 2$  --- $(2)$To solve for $u$ and $v$,mu

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$1$

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(B) Let $u = \frac{1}{x}$ and $v = \frac{1}{y}$.The given equations become:$3u - 2v = 5$  --- $(1)$$4u - 5v = 2$  --- $(2)$To solve for $u$ and $v$,multiply $(1)$ by $5$ and $(2)$ by $2$:$15u - 10v = 25$  --- $(3)$$8u - 10v = 4$  --- $(4)$Subtract $(4)$ from $(3)$:$(15u - 8u) = 25 - 4$$7u = 21 \implies u = 3$Substitute $u = 3$ into $(1)$:$3(3) - 2v = 5$$9 - 2v = 5$$-2v = -4 \implies v = 2$Thus,$\frac{1}{x} = 3$ and $\frac{1}{y} = 2$.The value of $\frac{1}{x} - \frac{1}{y} = 3 - 2 = 1$.

If $\frac{3}{x}-\frac{2}{y}=5$ and $\frac{4}{x}-\frac{5}{y}=2,$ then the value of $\frac{1}{x}-\frac{1}{y}$ is ............ $(x, y \neq 0)$

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