To solve this system of equations, we can start by isolating x in the first equation:

x = 7 + u

Next, we substitute this expression for x into the second equation:

(7 + u)^2 + u^2 = 9 - 2(7)(u)

Expanding and simplifying, we get:

49 + 14u + u^2 + u^2 = 9 - 14u

Combining like terms, we have:

2u^2 + 14u - 40 = 0

Dividing by 2 to simplify, we get:

u^2 + 7u - 20 = 0

Now, we can factorize this quadratic equation:

(u + 10)(u - 2) = 0

Setting each factor to zero, we solve for u:

u + 10 = 0 or u - 2 = 0
u = -10 or u = 2

Now that we have the values of u, we can find the corresponding values of x by using x = 7 + u:

If u = -10:
x = 7 - 10 = -3

If u = 2:
x = 7 + 2 = 9

Therefore, the solutions to the system of equations are:
x = -3, u = -10
x = 9, u = 2