Solving by elimination with two linear equations can be most easily described as adding the two together. The goal is to eliminate either the x or y variable, then solve for the remaining variable. Since neither coefficient are additive inverses ( 16x + 8x =/= 0), the easiest remedy is to multiple both sides of the second equation by 2.
2 (8x  6y) = 2(6) results in 16x  12y = 12
Now, add this to the first equation 16x  10y = 10:
16x  10y = 10
+ 16x  12y = 12
= 0x  22y = 22
Solve for y:
22y = 22 divide both sides by 22
y = 1
Now that you know y = 1, substitute it back into the original equation:
16x  10 (1) = 10
16x + 10 = 10
16x = 0
x = 0
To check, substitute x = 0 into the second original equation:
8 (0)  6y = 6
6y = 6
y = 1
I hope this is what you were looking for!
2/3/2014

David M.