由1式得X=Y+K,代入2式得
(Y+K)^2-8Y=0
Y^2+2KY-8Y+K^2=0
[Y+(K-4)]^2-(K-4)^2+K^2=0
[Y+(K-4)]^2=-8K+16
方程有一个实数解,-8K+16=0,解得K=2,代入上式解得Y=-2,代入1式解得X=4
结论:当K=2时方程组有一个实数解,此时方程的解为X=4,Y=-2