You need to put it in matrix form, then row reduce.

So, start with:

[1 1 6

4 -1 19]

Add row 1 to row 2:

[1 1 6

5 0 15]

Divide row 2 by 5:

[1 1 6

1 0 3]

Swap rows:

[1 0 5

1 1 6]

At this point, you have echelon form. The easiest way to go from here is to note x = 5, and substitute into y + x = 6.

However, if you need to be in reduced echelon form:

Subtract row 1 from row 2:

[1 0 5

0 1 1]

This gives you the two solution equations:

x = 5

y = 1

Hope this helps.