You have given one equation in two unknowns. You need two equations to solve a "system" of equations.
It's not difficult, you just haven't used all the information given in this word problem.
Let's put together the second equation, OK?
It comes from the week before. He worked 8 hours at the first job, so that is 8x. He worked 12 hours at the second job, so that is 12y. He made 171 dollars, so 8x + 12y = 171
Now you have two equations in two unknowns:
10x + 8y = 152.5
8x + 12y = 171
Solve one of the equations for either x or y. doesn't matter which equation, and it doesn't matter whether you solve for x or y.
Let's pick the first equation and solve for x.
10x = 152.5 - 8y
x = 15.25 - 0.8y
Substitute this into the second equation and you get
8(15.25 - 0.8y) + 12y = 171.
Now you can solve for the numerical value of y.
Substitute that into either equation and you can find the numerical value of x.
Good luck iwth your studies!