Question 1133746
<pre>{{{system((x+y)^2=144,x^2+y^2=80)}}}

{{{system(x^2+2xy+y^2=144,x^2+y^2=80)}}}

Subtract the two equations:

{{{(x^2+2xy+y^2)-(x^2+y^2)=144-80}}}

{{{x^2+2xy+y^2-x^2-y^2=64}}}

{{{2xy=64}}}

{{{xy=32}}}

{{{y=32/x}}}

Substitute in the original equation:

{{{x^2+y^2=80}}}

{{{x^2+(32/x)^2=80}}}

{{{x^2+1024/x^2=80}}}

{{{x^4+1024=80x^2}}}

{{{x^4-80x^2+1024=0}}}

{{{(x^2-16)(x^2-64)=0}}}

{{{(x-4)(x+4)(x-8)(x+8)=0}}}

x-4=0; x+4=0; x-8=0; x+8=0
  x=4;   x=-4;  x=8;   x=-8

Substitute each in {{y=32/x}}}

{{{y=32/4}}};{{{y=32/(-4)}}}; {{{y=32/8}}}; {{{y=32/(-8)}}}

{{{y=8}}};{{{y=-8}}}; {{{y=4}}}; {{{y=-4}}}

Solutions are

(x,y)=(4,8), (-4,-8), (8,4), (-8,-4)

Edwin</pre>