How do you solve for y: ##2x + y = 8## , ##2x – y = 8##?

You can solve this by Elimination Method .
Elimination Method:
Add this two equation together to eliminate ##y##
##2x+cancely = 8 ##
##2x -cancely = 8)##
##4x= 16##
##color(blue)(x= 4)##
Substitute ##x## in any of the equation say,
##2x+y = 8##
##2(4)+y = 8##
##8 + y =8## transposing 8 on the right side of the equation,
##color(blue)(y=0)##
Now, substitute the value of ##x and y## in any of the equations to verify if the answers are correct.
##2x+ y=8##
##2(4) + 0 = 8##
##color(red)(8=8)##