Question 812364
so as stated must have two zeros in one row and one in another such as the bottom left corner to make the matrix an upper triangle.. i will try answer this without making it to messy..

1. setup augmented matrix:
[A|b] = |12 2  2 |12|
        |60 12 24|48|
        |4  1  -1|-2|

2. apply row operations:
        |12 2  2 |12|
        |60 12 24|48|R2 = R2 - 5R1
        |4  1  -1|-2|R3 = 3R3 - R1
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        |12 2  2 |12  |
        |0  2  14|-12 |
        |0  1  -5|-18 |R3 = 2R3 - R2
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        |12 2  2  |12  |
        |0  2  14 |-12 |
        |0  0  -24|-18 |STOP: upper triangle matrix (three 0's in bottom left)
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now solve it start by backwards substitution.. find your Z value then Y then X