Questions: While building a medieval cathedral, it cost 37 guilders to hire 4 artists and 3 stonemasons, or 33 guilders for 3 artists and 4 stonemasons. What would be the expense of just 1 of each worker?

Determine the cost of hiring one artist and one stonemason.

Set up the system of equations.

The problem provides the following information:

1. Hiring 4 artists and 3 stonemasons costs 37 guilders:
   \( 4a + 3s = 37 \)
2. Hiring 3 artists and 4 stonemasons costs 33 guilders:
   \( 3a + 4s = 33 \)
   Thus, we have the system of equations:
   \[ \begin{align_} 4a + 3s &= 37 \quad \text{(1)} \\ 3a + 4s &= 33 \quad \text{(2)} \end{align_} \]

Solve the system of equations.

Using Gaussian elimination, we transform the augmented matrix:
\[ \left[ A | b \right] = \left[ \begin{array}{ccc} 4 & 3 & 37 \\ 3 & 4 & 33 \\ \end{array} \right] \]
After performing row operations, we arrive at:
\[ \left[ A | b \right] = \left[ \begin{array}{ccc} 1 & 0 & 7 \\ 0 & 1 & 3 \\ \end{array} \right] \]
This gives us the solutions:
\[ a = 7, \quad s = 3 \]

The cost of hiring one artist is \( 7 \) guilders and one stonemason is \( 3 \) guilders. Thus, the total expense for hiring one of each worker is:
\[ \boxed{7 + 3 = 10} \]

The total expense for hiring one artist and one stonemason is \( \boxed{10} \).