Question

Identify the solution(s) of the system of equations, if any. -4x-2y=16 2y=-4x-16

Answer 1

-4x-2y = 16
2y = -4x-16

Get one variable alone on both equations

-4x - 16 = 2y
-4x - 16 = 2y

You'll realize that they're the same equation.
Use substitution

-4x-16 = -4x-16
0 = 0
x = all solutions

Use x = all solutions in an earlier equation to find y

-4x - 16 = 2y
SInce x can be all solutions y is also all solutions
y = all solutions

Answer 2

-4x - 2y = 16
2y = -4x - 16
 2           2
  y = -2x - 8

-4x -2(-2x - 8) = 16
-4x + 4x + 16 = 16
0x + 16 = 16
      - 16 - 16
         0x = 0
          0     0
           x = 0
2y = -4x - 16
2y = -4(0) - 16
2y = 0 - 16
2y = -16
 2       2
  y = -8
(x, y) = (0, -8)