Solving system of equations by echelon form.

Question

I have an example of a solution for a system of equations and there is a step I do not understand:

Could anyone offer some help please?

Kind regards Stany

Answer 1

$$ \begin{aligned} \left(\begin{array}{cccc} 1 & 1 & 1 & 0 \\ 3 & -1 & 1 & 20 \\ 6 & 2 & -1 & 40 \end{array}\right) & \rightarrow\left(\begin{array}{cccc} 1 & 1 & 1 & 0 \\ 0 & -4 & -2 & 20 \\ 0 & -4 & -7 & 4 \end{array}\right) \\ & \rightarrow\left(\begin{array}{cccc} 1 & 1 & 1 & 0 \\ 0 & -4 & -2 & 20 \\ 0 & 0 & -5 & 20 \end{array}\right) \\ \therefore-5 z=20 & \Rightarrow z=-4 \\ -4 y-2 x(-4)=20 & \Rightarrow y=-3 \\ x-3-4=0 & \Rightarrow x=7 \end{aligned} $$ Hence $(x,y,z)=(7,-3,-4).$