x+7y=13
x-7y=5

To solve, just use substitution.

Solve one equation for y or x and sub into the other.

You can also eliminate either x or y like this;

x+7y=13
x-7y=5

(x+x) + (7y + -7y) = (13+5)

then,

2x + 0y = 18

Can you continue?

OR

(x-x) + (7y - -7y) = (13-5)

0x + 14y = 8

Here also, can you continue?