Solve the following systems of equations:

Question:

Solve the following systems of equations:

$\frac{2}{x}+\frac{5}{y}=1$

$\frac{60}{x}+\frac{40}{y}=19, x \neq 0, y \neq 0$

 

Solution:

The given equations are:

$\frac{2}{x}+\frac{5}{y}=1$$\ldots(i)$

$\frac{60}{x}+\frac{40}{y}=19 \ldots(i i)$

Multiply equation $(i)$ by 8 and subtract (ii) from equation (i), we get

$-\frac{44}{x}=-11$

$\Rightarrow x=4$

Put the value of $x$ in equation $(i)$, we get

$\Rightarrow \frac{2}{4}+\frac{5}{y}=1$

$\Rightarrow \frac{5}{y}=1-\frac{2}{4}$

$\Rightarrow \frac{5}{y}=\frac{1}{2}$

$\Rightarrow y=10$

Hence the value of $x=4$ and $y=10$.

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