{(х-1)(у-1)=2 {х+у=5

Question

{(х-1)(у-1)=2 {х+у=5

Answer 1

( Х - 1 )( y - 1 ) = 2
xy - x - y + 1 = 2
••••••
X + y = 5
X = 5 - y
•••••••
y( 5 - y ) - ( 5 - y ) - y + 1 = 2
5y - y^2 - 5 + y - y + 1 = 2
5y - y^2 - 4 = 2
y^2 - 5y + 6 = 0
D = 25 - 24 = 1
y1 = ( 5 + 1 ) : 2 = 3
y2 = ( 5 - 1 ) : 2 = 2
••••••
X = 5 - y
X1 = 5 - 3 = 2
X2 = 5 - 2 = 3
Ответ ( 2 ; 3 ) ; ( 3 ; 2 )