`2x-y+3z=24`

`2y-z=14`

`7x-5y=6`

Write the equations as,

`[[2,-1,3,|24],[0,2,-1,|14],[7,-5,0,|6]]`

Make the pivot in the first column by dividing the First row by 2,

`[[1,-1/2,3/2,|12],[0,2,-1,|14],[7,-5,0,|6]]`

Multiply the first row by 7,

`[[7,-7/2,21/2,|84],[0,2,-1,|14],[7,-5,0,|6]]`

Subtract the 1st row from the 3rd row and restore it,

`[[1,-1/2,3/2,|12],[0,2,-1,|14],[0,-3/2,-21/2,|-78]]`

Make the pivot in the second column by dividing the 2nd row by 2,

(The entire section contains 182 words.)

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