2x+5y=11 and 4x+3y=1 solve with elimination

Multiply you first equation by 2 to get 4x + 10y = 22
Now the x terms can be eliminated and cancelled out using elimination.
4x + 10y = 22
4x + 3y = 1

To eliminate you need to "subtract", so you need to multiply one of the equations by -1. 

4x + 10y = 22
-4x -3y = -1

0 + 7y = 21
y = 3

Now plug 3 into either one of the equations to get x.