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If 32x-y = 3x+y = $$\sqrt {27} {\text{,}}$$  the value of y is = ?

If 32x-y = 3x+y = $$\sqrt {27} {\text{,}}$$  the value of y is = ? Correct Answer $$\frac{1}{2}$$

$$\eqalign{ & {{\text{3}}^{2x - y}}{\text{ = }}{{\text{3}}^{x + y}}{\text{ = }}\sqrt {{3^3}} = {3^{\frac{3}{2}}} \cr & \Leftrightarrow 2x - y = \frac{3}{2}and \,\,x + y = \frac{3}{2} \cr & \Leftrightarrow 3x = \frac{3}{2} + \frac{3}{2} = 3 \cr & \Leftrightarrow x = 1 \cr & \therefore y = \left( {\frac{3}{2} - 1} \right) = \frac{1}{2} \cr} $$

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