Adding the two linear equations won't do anything, because all the coefficients are positive, so we can't remove any variable doing that.
How to refute the claym?
We have the system of equations:
12x + 2y = 30
10x + y = 26
The student claims that we need to add two times the second line to the first one.
The problem here is that if we do that, nothing happens, because all the coefficients are positive, so we won't remove any variable.
What we need to do is subtract two times the second equation for the first one.
Then we will get:
(12x + 2y) - 2*(10x + y) = 30 - 2*26
12x + 2y - 20x - 2y = -22
-8x = -22
In this way we removed the variable y.