一條數唔識計~~f.4既

Differentiate (1), we have
2x=5+(dy/dx)
dy/dx=2x-5 ......(3)
Differentiate (2), we have
0+dy/dx=5
dy/dx=5...........(4)
From (3) and (4),
2x-5=5
x=5.................(5)
sub. (5) into (1)
y=16...............(6)
sub (5) and (6) into (2)
k+16 = 25
Therefore k=9

X^2 + 16 = 5X + Y .....(1)
k + Y = 5X .......(2)

From (2), we have Y = 5X - k.
Putting it into (1):
X^2 + 16 = 5X + (5X - k)
X^2 - 10X + (16 + k) = 0
As the set of simutaneous equations have one unique solution,
distriminant = 0
(-10)^2 - 4 (1) (16 + k) = 0
k = 100/4 - 16
k = 9.

put the 2nd equation into the 1st one

X^2 + 16 = (K + Y) + Y
X^2 + 16 = K + 2Y
K = X^2 - 2Y +16