Solve the system: x + y = 10 and 2x - y = 5.

Add the two equations to eliminate y:
x + y = 10
2x - y = 5

Adding gives:
3x = 15

Divide by 3:
x = 5

Substitute x = 5 into the first equation:
5 + y = 10

Subtract 5:
y = 5

Therefore, the solution to the system is the ordered pair (5, 5).