\left \{ {{x^{2} + y^{2}=65 } \atop {y=2x-15}} \right. \\ \\ x^{2} +(2x-15)^2=65 \\ x^2+4x^2-60x+225-65=0 \\ 5x^2-60x+160=0 \\ x^2-12x+32=0 \\ \\ D=144-4*32=144-128=16 \\ \\ x_{1}= \frac{12+4}{2}=8 \\ \\ x_{2}= \frac{12-4}{2}=4 " alt=" \left \{ {{ x^{2} + y^{2}=65 } \atop {2x-y=15}} \right. => \left \{ {{x^{2} + y^{2}=65 } \atop {y=2x-15}} \right. \\ \\ x^{2} +(2x-15)^2=65 \\ x^2+4x^2-60x+225-65=0 \\ 5x^2-60x+160=0 \\ x^2-12x+32=0 \\ \\ D=144-4*32=144-128=16 \\ \\ x_{1}= \frac{12+4}{2}=8 \\ \\ x_{2}= \frac{12-4}{2}=4 " align="absmiddle" class="latex-formula">
При x=8, y=16-15=1
При х=4, у=8-15=-7
Ответ: (8;1) и (4;-7)