To solve the first equation, 3 sqrt(x) - 8 = 0, we first isolate the square root term:

3 sqrt(x) = 8

Then, divide both sides by 3 to solve for x:

sqrt(x) = 8/3

Square both sides to eliminate the square root:

x = (8/3)^2
x = 64/9

Now, for the second equation, sqrt(5x-6) = 1, we square both sides to eliminate the square root:

5x - 6 = 1

Add 6 to both sides:

5x = 7

Divide by 5 to solve for x:

x = 7/5

Therefore, the solution to the system of equations is x = 64/9 and x = 7/5.