Starting system:

2y + 4x = -6 6x - 2y = 16

In this example, we use the "addition" method. First, re-arrange 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