Hi, I've got so far try to solve simultaneous congruence equations but have run a ground.

Question is solve the simultaneous equations

7x=3mod34 and x=7mod41

I've solved the first one to get x=15mod 34 hence x= 34u+15

The second is x=7 mod 41

Thus I've put 34u+15=7mod 41

Now at this point I thought it would go to 34u=33mod41 but if this is the case then I'm struggling to solve for u. I think I've made a mistake at 34u+15=7 mod 41 but not sure what.