math,algebra II

I need someone to explain to me step by step the process of this problem its in my book as an example but i am not understanding it. Ive researched the explanation of the ECHELON METHOD...BUt i am not seeingit...this is the problem that they have:

Use the echeclon method to solve the system of three equations in three unknowns

2x+4y+z = 22
4x - 4y -z = 2
4x +y =4z = 12

Matrix would be the prefered method, echelon is harder.

First, take eq1)
2x+4y+z = 22 add this to equation 2 to eliminate z
2x+4y+z = 22
4x - 4y -z = 2
6x=24 solve for x.

Now multipy equation 2) by 4
16x-16y-4z=8
add to equation three
4x +y +4z = 12 or
20x-15y=20 you know x, so solve for y.

Put x,y in any of the equations, solve for z.

This was NOT a good problem for echelon.

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