How to solve the system of equations?

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How can I solve this system of equations? (without using any software of course)

$$\ e^{-y} \cos(x)= \frac{5 \pm3}{4} \quad\text{and}\quad\ e^{-y} \sin(x)=0$$

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Hint: square each equation and add them together. This will eliminate $x$ because $\sin^2 x + \cos^2 x = 1. $