How do you solve this system of equations

Can you please help me solve this...THANKS!!

x^2 + y^2 = 34
x + y = 8

x + y = 8 -------> y = 8 - x

Replace y in first equation with (8-x), then solve for x:
x^2 + (8-x)^2 = 34
x^2 + 64 - 16x + x^2 = 34
2x^2 - 16x + 30 = 0
2 (x^2 - 8x + 15) = 0
2 (x - 3) (x - 5)

x = 3 or 5

When x = 3, y = 8 - 3 = 5
When x = 5, y = 8 - 5 = 3

Solutions are: (3, 5) and (5, 3)

Solve for y using second equation: y = 8-x
Plug that into the first equation x^2 + (8-x)^2 = 34
Solve for x. You should get two answers.
Plug each into the second equation to get the two answers for y corresponding to each x.

from the 2nd, y = 8 - x
replace y in the first with this expression
x^2 + (8-x)^2 = 34
x = 4 is a repeated solution of this equation
if x = 4 from the second expression, y = 4 also
(4,4) is the solution point