solve the system of equations

Hello ballhopper!

{ y^2 + x^2 = 10

y+x = 4

\(y^{2}+x^{2}=10 \) 

\(y+x=4\)

\(y=4-x\)

\(\left(4-x\right) ^{2}+x^{2}=10 \)

\(16-8x+x²+x²=10 \)

\( 8-4x+x² =5 \)

\( x²-4x+3=0 \)

\( ax²+bx+c=0 \)

\( a=1; \ b=-4; \ c=3\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {4 \pm \sqrt{16-12} \over 2}\) 

\(x_{1} = {4 + \sqrt{16-12} \over 2}=3\)

\(x_{2} = {4 - \sqrt{16-12} \over 2}=1\)

\(solution\ set = \{3 ;1\}\)

Greeting asinus :- )  !