Ответ: x=6 ; y=10

[tex]\left \{ {{(15 - x) {}^{2} - {(5 + x)}^{2} = - 4y } \atop {4x - 3y + 6 = 0}} \right. \\ \\ \left \{ {{225 - 30x + {x}^{2} - 25 - 10x - {x}^{2} = - 4y } \atop {4x - 3y = - 6 }} \right. \\ \\ \left \{ {{ - 40x + 200 = - 4y} \atop {4x - 3y = - 6}} \right. \\ \\ \left \{ {{ - 40x + 4y = - 200} \atop {4x - 3y = - 6 \: \: \: \times 10| }} \: \: \ \right. \\ \\[/tex]

[tex]\left \{ {{ - 40x + 4y = - 200} \atop {40x - 30y = - 60}} \right. + \\ \\ - 26y = - 260 \\ y = 10[/tex]

И вместо у поставим 10

[tex]4x - 3y = - 6 \\ 4x - 3 \times 10 = - 6 \\ 4x - 30 = - 6 \\ 4x = 24 \\ x = 6[/tex]