[tex]x-y=11\to x=11+y\\\\x^2-y^2=55\\\\\Downarrow\ substitute\\\\(11+y)^2+y^2=55\\\\11^2+2\cdot11\cdot y+y^2+y^2-55=0\\\\2y^2+22y+121-55=0\\\\2y^2+22y+66=0\ \ \ /:2[/tex]
[tex]y^2+11y+33=0\\\\a=1;\ b=11;\ c=33\\\\\Delta=b^2-4ac;\ \Delta=11^2-4\cdot1\cdot33=121-132=-11 < 0\\\\y^2+11y+33=0-false\\\\y\in\O[/tex]
