BuddyBoy

We complete the square for the first equation by observing that the first equation is equivalent to\[ (x^2-10x +25) +(y^2-4y +4)=36, \]which is also equivalent to\[ (x-5)^2 +(y-2)^2 =6^2. \]Similarly, the equation for the second circle is\[ (x+7)^2 +(y+3)...

The graph of the two inequalities is shown below: [asy] Label f; f.p=fontsize(4); xaxis(-3,3,Ticks(f, 1.0)); yaxis(-0,4,Ticks(f, 1.0)); fill((0,0)--(-1.5,1.5)--(0,3)--(1.5,1.5)--cycle, grey); draw((0,0)--(-3,3), Arrow); draw((0,0)--(3,3), Arrow); draw((0,...