You need to form the matrix of the system using the coefficients of variables `x_1,x_2,x_3` such that:

`A = ((1,-5,4),(2,-7,3),(2,-1,-7))`

You need to evaluate determinant of the matrix such that:

`Delta=[[1,-5,4],[2,-7,3],[2,-1,-7]]`

`Delta = 49 - 8 - 30 + 56 + 3 - 70`

`Delta = -108 + 108 = 0`

Since `Delta=0` , the system has not only one solution.

You need to identify if the system has more than one solution or it is indeterminate.

You should select a minor such that:

`delta = [[1,-5],[2,-7]] = -7 + 10 != 0`

You need to evaluate characteristic determinant such that:

`char = [[1,-5,-3],[2,-7,-2],[2,-1,1]]` = `-7 + 6 + 20 - 42 - 2 + 10 != 0`

**Since the characteristic is not zero, then the system has no solution.**

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