X - the rate charged by the first mechanic
y - the rate charged by the second mechanic
The sum of the two rates was $155.
The first mechanic worked for 10 hours, the second mechanic worked for 5 hours, and together they charged $1000.
Set 155-x and 200-2x equal to each other:
The rate charged by the first mechanic was $45, and the rate charged by the second mechanic was $110.