let

x = the hourly labor cost of the electrician per hour

y = the hourly labor cost of the apprentice per hour

on the first job the electrician works five hours and the apprentice works four hours

5x + 4y = 270

on the second customer was billed 369 for labor

since we know that they worked 5 hours in total for the first and the second job

then it turns out that the apprentice worked alone 1 hour on the second job and

y = 369

by solving the system of equations

5x + 4y = 270

y = 369

we get negative results for x

possible error in the text of question

There is simply not enough information to solve this problem. Specifically, the number of hours worked by the electrician and the number of hours worked by the apprentice for the $369 billing must be stated so that there are two equations with two unknowns.

As stated, the problem provides two equations with four unknowns, completely unsolvable.

let 'x' represent the hourly rate of the electrician and 'y' represent the hourly rate of the apprentice

let 'a' represent the hours worked by the electrician on the second job and 'b' represent the hours worked by the apprentice

we then have these equations:

4x+5y=270

ax+by=369