What is the solution to the following system of equations? 3x-4y=35 and 3x+4y=5

3x - 4y = 35
3x + 4y = 5
add
6x = 40
x = 40/6 which reduces to 20/3

3x - 4y = 35
3(20/3) - 4y = 35
20 - 4y = 35
-4y = 35 - 20
-4y = 15
y = -15/4

solution is (20/3, -15/4)

Note that -4y appears in the first equation and +4y in the second.
Adding the two equations together will eliminate y from both equations:

3x-4y=35
3x+4y=5

6x     =40
     40
x=---    or (20/3).
     6

Go back to the original equations.  Choose either one.  Subst. x = 20/3 into that equation and solve for y.

Then write your solution in the form (20/3,   y  ).