Because mathematicians are lazy I will not write "mod 35" rather I will write, and you will know it is modulo 35.

Now, we have.

Multiply the first equation by 13, second by -5,

Note I reduced everything to its smallest positive integer.

Add them, (note )

Put that into any equation, say the first.

Since,

And divides 20.

We will have 5 incongruent solutions.

You should be able to solve those.