Solve for the value of u and t in the following equation U^2-t=6+u........(1) t+u=3......(2)?

Assuming that U = u

Let' make the first equation look a bit more convenient
u^2 - t = 6 + u
u^2 - t - u = 6
u^2 - (t + u) = 6

Now we add the second equation to the first:

1) u^2 - (t + u) = 6
2) t + u = 3
-------------------------
3) u^2 = 9 ;; take the square root

u = 3

Insert the value of u into the second equation to get t:

t + 3 = 3
t = 0

Done.