please help me with these questions!!

For the 1st question:

Square the 1st equation.

(x+y)^2=256

x^2 + 2xy + y^2=256

Substitute x^2 + y^2 = 128

2xy + 128 = 256 <---- That goes back from second-order to first-order.

2xy = 128

xy = 64

y = 64/x ---(3)

Substitute (3) into x+y = 16
x + 64/x = 16

x^2-16x + 64 = 0 <---- That goes back from first-order to second-order, funny.

(x-8)^2=0

x-8 = 0

x = 8

y = 64/8 = 8

For the second question:

Square the 2nd equation:

(x+y)^2=16

x^2 + 2xy + y^2 = 16

Substitute x^2 + y^2 = 8

2xy + 8 = 16

2xy = 8

xy = 4

y = 4/x

Substitute this into the 2nd equation:

x + 4/x = 4

x^2 - 4x + 4 = 0

(x-2)^2=0

x - 2 = 0

x = 2

y = 4/2 = 2