16x-10y=10 and -8x-6y=6
The coefficients of x are 16 and -8. To apply elimination, these should be the same. Positives and negatives are non-issues.
Let's take the first equation...
16x-10y=10
Let's multiply both sides by 1/2...
(1/2)(16x-10y)=(10)(1/2)
8x-5y=5
Let's add this to the second equation...
-8x-6y=6
8x-5y=5
0-11y=11
The x is eliminated...
-11y=11
Let's divide both sides by -11...
(-11y)/11=11/-11
y=-1
Let's plug this into either original equation to establish the value of x. I randomly select the second...
-8x-6y=6
-8x-[(6)(-1)]=6
-8x-(-6)=6
Subtracting a negative number is identical to adding a positive number...
-8x+6=6
Let's subtract 6 from both sides...
-8x+6-6=6-6
-8x=0
x=0
Let's plug both values into the first equation to verify results...
16x-10y=10
[(16)(0)]-[(10)(-1)]=10
0-(-10)=10
10=10