Algebra 1 5x+y=6 5x+3y=-5 the y-coordinate of the solution to the system shown a) -5 b) -1 c) 1/2 d) 1

Subtract the equations straight down. So we'll subtract the x terms together
5x - 5x = 0x = 0 
meaning the x terms effectively go away after subtraction

Then we do the y terms together in the same exact order
y-3y = -2y

Then finally the right hand side values
6 - (-5) = 6+5 = 11

All of that work done indicates we have 0x-2y = 11 which is the same as -2y = 11. Divide both sides by -2 and we end up with y = -11/2

This answer isn't listed so I'm thinking there's a typo your teacher made somewhere.

Where is the diagram?