Question 1120970
The difference of squares says that x<SUP>2</SUP>-y<SUP>2</SUP>=(x+y)(x-y). 

{{{system(x^2-y^2=24,x+y=8)}}}

{{{system((x+y)(x-y)=24,x+y=8)}}} Substitute 8 for x+y in the first equation,

{{{system(x-y=3,x+y=8)}}} Add both equations to get

{{{2x=11}}}

{{{highlight(x=5.5)}}} 

{{{5.5-y=3}}}

{{{highlight(y=2.5)}}} Check:5.5+2.5=8 5.5<sup>2</sup>-2.5<sup>2</sup>=24 24=24. Graph:

{{{graph(450,450,-10,10,-10,10,y=sqrt(x^2-24),y=8-x)}}}