[tex]\displaystyle\bf\\\left \{ {{x^{2} -xy+y^{2} =63} \atop {y-x=3}} \right. \\\\\\\left \{ {{x^{2} -x\cdot(x+3)+(x+3)^{2} =63} \atop {y=x+3}} \right. \\\\\\\left \{ {{x^{2} -x^{2} -3x+x^{2} +6x+9-63=0} \atop {y=x+3}} \right. \\\\\\\left \{ {{x^{2} +3x-54=0} \atop {y=x+3}} \right. \\\\\\\left \{ {{\left[\begin{array}{ccc}x_{1} =-9\\x_{2} =6\end{array}\right } \atop {y=x+3}} \right.[/tex]

[tex]\displaystyle\bf\\\left[\begin{array}{ccc}\left \{ {{x_{1} =-9} \atop {y_{1} =-9+3}} \right. \\\left \{ {{x_{2} =6} \atop {y_{2} =6+3}} \right. \end{array}\right\\\\\\\left[\begin{array}{ccc}\left \{ {{x_{1} =-9} \atop {y_{1} =-6}} \right. \\\left \{ {{x_{2} =6} \atop {y_{2} =9}} \right. \end{array}\right\\\\\\Otvet \ : \ (-9 \ ; \ -6) \ \ , \ \ (6 \ ; \ 9)[/tex]