[tex]x^2+y^2=225 \\
x-7y=-75 \\ \\
\hbox{solve the second equation for x:} \\
x-7y=-75 \ \ \ |+7y \\
x=7y-75 \\ \\
\hbox{substitute 7y-75 for x in the first equation:} \\
(7y-75)^2+y^2=225 \\
49y^2-1050y+5625+y^2=225 \\
50y^2-1050y+5625=225 \ \ \ \ \ \ \ \ \ |-225 \\
50y^2-1050y+5400=0 \ \ \ \ \ \ \ \ \ \ \ \ |\div 50 \\
y^2-21y+108=0 \\
y^2-9y-12y+108=0 \\
y(y-9)-12(y-9)=0 \\
(y-12)(y-9)=0 \\
y-12=0 \ \lor \ y-9=0 \\
y=12 \ \lor \ y=9[/tex]
[tex]x=7y-75 \\
x=7 \times 12 -75 \ \lor \ x=7 \times 9-75 \\
x=84-75 \ \lor \ x=63-75 \\
x=9 \ \lor \ x=-12 \\ \\
(x,y)=(9,12) \hbox{ or } (x,y)=(-12,9)[/tex]
The points are (9,12) and (-12,9).
The answer is A.
