How to solve a system of equations with sin and cos?

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$50= 35\cos(x) +25\cos(y) $

$0= 35\sin(x)+25\sin(y) $

Thanks!

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There are several approaches. You could just use $\cos x = \pm \sqrt {1-\sin^2 x}$ and get a system in just $\sin x, \sin y$. In this case I would square the two equations and add, then square them and subtract. Magic happens.