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x²+y²=41
x-y=9
despejamos x,en la segunda ecuacion y la sustituimos en la primera
x-y=9
x=y+9
x=y+9
x²+y²=41
(y+9)²+y²=41
y²+18y+81+y²=41
y²+y²+18y+81-41=0
2y²+18y+40=0 dividimos todo entre 2
y²+9y+20=0
(y+4)(y+5)=0
y+4=0 y+5=0
y= -4 y= -5
si y= -4
x-y=9
x-(-4)=9
x+4=9
x=9-4
x=5
si y= -5
x-y=9
x-(-5)=9
x+5=9
x=9-5
x=4
tu conjunto de soluciones son
x=5 y= -4
x=4 y= -5