You can use an elimination or a substitution.

Elimination:

x + y = 10
x - y = 6
2x + 0 = 16

or


x + y = 10
-x + y = -6
0 + 2y = 4

Substitution:
x - y = 6
x = 6 - y

Plug in the first equation:
(6 - y) + y = 10

There are many ways to solve simultaneous equations. You just do the one you're more confident with.