To solve this system of equations, we can use a method called substitution or elimination.

First, let's use the elimination method to solve this system of equations.

3x + 4z = 85
5x + 4z = 107

We need to eliminate one of the variables. We can do this by subtracting the first equation from the second equation:

(5x + 4z) - (3x + 4z) = 107 - 85
2x = 22
x = 11

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for z. Let's use the first equation:

3(11) + 4z = 85
33 + 4z = 85
4z = 52
z = 13

Therefore, the solution to the system of equations is x = 11 and z = 13.