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Maple can solve a system of equations such as $\sin x + y =0, \sin x - y =0$. However,

var('x y') solve([sin(x) + y ==0, sin(x) - y==0], [x, y]) produces no useful answer.

Is there any other way to proceed?

Maple can solve a system of equations such as $\sin x + y =0, \sin x - y =0$. However,

var('x y') solve([sin(x) + y ==0, sin(x) - y==0], [x, y]) produces no useful answer.

Is there any other way to proceed?