Verified answer

x²+y²=100

x+y=14

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x=14-y

(14-y)²+y²=100

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x=14-y

196-28y+y²+y²=100

2y²-28у+196-100=0

2у²-28у+96=0

у²-14у+48=0

D/4=7²-48=1

у1=7-1=6

у2=7+1=8

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у1=6

х1=14-6

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у1=6

х1=8

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у2=8

х2=14-8

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у2=8

х2=6

(8; 6) ∪ (8; 6)