Starting system: 

In this example, we use the "addition" method. First, rearrange the equations so each column is devoted to at most one variable:
4x + 2y = 6 6x  2y = 16 
Add the terms in each column:
10x + 0y = 6 + 16
10x = 10
x = 1
Substitute "1" for "x" in the top original equation, to get:
4(1) + 2y = 6
2y = 6  4 = 10
y =  5