Yequals x + z + 5 z equals -3 y - 3 2x minus y equals negative 4 how can i solve using 3 variable systems of equation

To solve a set of linear equations in 3 variables, you need 3 equations. As far as I can tell, you have 2 equations here, so the best you can do is write expressions for 2 of the variables in terms of the third.

If you have
  x +z +5z = -3y -3
  3x -y = -4
Then you can rewrite as
  x = -1.5 -0.6z
  y = -0.5 -1.8z


You can get this by any of the usual methods of solving linear equations. Just treat the system as two equations in x and y with the z terms on the right side of the equal sign:
  x +3y = -3 -6z
  3x -y = -4