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Verified answer

[tex]\displaystyle \left \{ {{2u+5y=6} \atop {3u+7y=5}} \right.\\ \\7(2u+5y)-5(3u+7y)=7*6-5*5\\-u=17\\u=-17\\2u+5y=6\\y=8\\(u,y)=(-17,8)[/tex]