Three equation solving analytically in Mathematica

Question

Im doing coding in iterative schemes but I do not know to solve three equations analytically in Mathematica step by step. For example I given thre equations in the attached figure. I want to solve these for $x,y,z$ step by step in Mathematica

Answer 1

Using function displayRREF you can see the step by step as follows

eqs = {3 x + 2 y + 4 z == 1, -x + y + 2 z == 2, x - 3 y + z == -1}
{b, A} = CoefficientArrays[eqs, {x, y, z}];
displayRREF[A, -b]

Answer 2

WolframAlpha["solve 3x+2y+4z == 1, -x+y+2z == 2, x-3y+z == -1"]

{3 x + 2 y + 4 z == 1, -x + y + 2 z == 2, x - 3 y + z == -1} /.
 {x -> -3/5, y -> 11/35, z -> 19/35}
(* {True, True, True} *)