If 2/x + 3/y = 6 and 1/x + 1/(2y) = 2 then

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bb(x = $\frac{2}{3}$, y = 1) Explanation: Put a = 1/x and b = 1/y. Then 2a + 3b = 6 and a + ($\frac{1}{2}$)b = 2. Multiply the second equation by 2: 2a + b = 4 Subtract from the first: 2b = 2 $\Rightarrow$ b = 1 $\Rightarrow$ y = 1 Substitute back: 2a + 1 = 4 $\Rightarrow$ a = $\frac{3}{2}$ $\Rightarrow$ x = $\frac{2}{3}$

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