Gregg O. answered • 07/27/15

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|1 1 1 1|

|3 -1 -1 4|

|1 5 5 -1|

Subtract 3R1 from R2. Subtract R1 from R3:

|1 1 1 1|

|0 -4 -4 1|

|0 4 4 -2|

Multiply R1 by 4:

|4 4 4 4|

|0 -4 -4 1|

|0 4 4 -2|

Add R1 and R2, and place the result in R1. Add R3 and R2, and place the result in R3:

|4 0 0 5|

|0 -4 -4 1|

|0 0 0 -1|

That last row of all 0s for your variable coefficients, coupled with a -1 for your constant, lets you know it's an inconsistent system. No solution.