Final answer:
To solve the system using an augmented matrix, perform row operations to eliminate the leading coefficients and arrive at the reduced-row echelon form of the augmented matrix.
Step-by-step explanation:
To solve the system of equations using an augmented matrix, let's write the system of equations in the form of AX = B, where A represents the coefficients, X represents the variables, and B represents the constant terms:
[-1 -3 | -17]
[2 -6 | -26]
Next, we will use row operations to transform the augmented matrix into row-echelon form or reduced-row echelon form. Using these operations, we can eliminate the leading coefficient in the second row:
[1 3 | 17]
[0 -12 | -10]
Continuing with the row operations, we can divide the second row by -12 to get:
[1 3 | 17]
[0 1 | 5/6]
Finally, by performing the appropriate row operation, we can eliminate the leading coefficient in the first row:
[1 0 | 4]
[0 1 | 5/6]
Therefore, the solution to the system of equations is x = 4 and y = 5/6. Hence, the correct answer is option B) x = -3, y = 5.