Відповідь:

x = 11, y = 5

Пояснення:

[tex]\left \{ {{x - y = 6} \atop {x^{2} - y^{2} =96}} \right.[/tex]

[tex]\left \{ {{x = 6 + y} \atop {x^{2} - y^{2} =96}} \right.[/tex]

[tex]\left \{ {{x = 6 + y} \atop {(6 + y)^{2} - y^{2} =96}} \right.[/tex]

[tex]\left \{ {{x = 6 + y} \atop {36 + 12y + y^{2} - y^{2} =96}} \right.[/tex]

[tex]\left \{ {{x = 6 + y} \atop {12y = 60} \right.[/tex]

[tex]\left \{ {{x = 6 + y} \atop {y = 5} \right.[/tex]

[tex]\left \{ {{x = 6 + 5} \atop {y = 5} \right.[/tex]

[tex]\left \{ {{x = 11} \atop {y = 5} \right.[/tex]