Final answer:
The linear system of equations does not have a solution, indicated by a contradiction in the Gauss elimination process, where an abnormal row suggests that a solution is not possible.
Step-by-step explanation:
In order to assess the solvability of the linear system of equations and employ Gauss elimination to find solutions, the system is initially transformed into an augmented matrix:
2 5 4 5 | -5
2 3 3 -1 | 7
2 3 3 4 | 3
2 -1 5 -4 | 21
Initiating the Gauss elimination, the first column is already set as a pivot (2). Subsequent steps involve subtracting the first row from the second, third, and fourth rows to yield:
2 5 4 5 | -5
0 -2 -1 -6 | 12
0 -2 -1 -1 | 8
0 -6 1 -9 | 26
Continuing the process, the second column's pivot is chosen as -2, and further operations lead to:
2 5 4 5 | -5
0 -2 -1 -6 | 12
0 0 0 -7 | 20
0 0 -2 -27 | 62
For the third column, the number -2 can be our pivot for the fourth row. We can change the fourth row by adding the third row to it:
2 5 4 5 | -5
0 -2 -1 -6 | 12
0 0 0 -7 | 20
0 0 -2 -34 | 82
However, we encounter an abnormal row which implies a contradiction (0 = 82), hence, the original system has no solution.