Final answer:
To solve the system of equations, use Gaussian elimination to transform the augmented matrix into reduced row-echelon form. The solution is (1, -1, -4).
Step-by-step explanation:
To solve the system of equations, we will use the method of Gaussian elimination. We will first write the augmented matrix for the system of equations:
[2 1 1 | -3]
[3 -5 3 | -4]
[5 -1 2 | -3]
Next, we will perform row operations to transform the augmented matrix into reduced row-echelon form:
[1 0 0 | 1]
[0 1 0 | -1]
[0 0 1 | -4]
The solution to the system of equations is (1, -1, -4), so the correct answer is Option A (1,-1,-4).