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solve system of equation

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hi

could you help me to solve this problem

dose the following problem has solution?and how can i write it in maple?

this is a problem 6 equation and 4 unknown variable

sys := 1.20710678118654752440084436211*x-.207106781186547524400844362106*y = 1, -1.20710678118654752440084436210*x+1.20710678118654752440084436210*z+.207106781186547524400844362105*y-.207106781186547524400844362105*w+1.61353108866376978508023871599*z-1.61353108866376978508023871599*w = 0, 1.41421356237309504880168872421*x-1.41421356237309504880168872421*z-1.41421356237309504880168872421*y+1.41421356237309504880168872421*w-1.37455258362134694054214893147*z-1.37455258362134694054214893147*w = 0, -1.20710678118654752440084436210*x-1.20710678118654752440084436210*z+.207106781186547524400844362105*y+.207106781186547524400844362105*w+.238978505042422844538089784517*x-.238978505042422844538089784517*y = 0, 1.41421356237309504880168872421*x+1.41421356237309504880168872421*z-1.41421356237309504880168872421*y-1.41421356237309504880168872421*w+1.37455258362134694054214893147*x-1.37455258362134694054214893147*x = 0


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