[tex]x^2 + y^2= 25\\
2x+y=10\\\\
x^2 + y^2= 25\\
y=10-2x\\\\
x^2+(10-2x)^2=25\\
x^2+100-40x+4x^2=25\\
5x^2-40x+75=0\\
x^2-8x+15=0\\
x^2-3x-5x+15=0\\
x(x-3)-5(x-3)=0\\
(x-5)(x-3)=0\\
x=5 \vee x=3\\\\
y=10-2\cdot5 \vee y=10-2\cdot3\\
y=0 \vee y=4\\\\
\boxed{(x,y)=\{(3,4),(5,0)\}}
[/tex]
