Final answer:
To solve the system using an augmented matrix, convert the system of equations to a matrix and perform row operations to reduce it. The solution is x = -17/5 + 1/5y + 3/5z, y = -9z + 9, and z is any real number.
Step-by-step explanation:
To solve the system using an augmented matrix, we need to write the system of equations in matrix form, where the coefficients of the variables are the entries of the matrix. The augmented matrix will have the form:
[5 -1 -3 -17]
[1 0 -6 -26]
Next, we perform row operations to row reduce the matrix. We can start by multiplying the first row by 1/5 to make the first entry 1.
[1 -1/5 -3/5 -17/5]
[1 0 -6 -26]
Now we can multiply the first row by -1 and add it to the second row to eliminate the first variable in the second equation.
[1 -1/5 -3/5 -17/5]
[0 1 -9 -9]
The reduced matrix corresponds to the system:
x - 1/5y - 3/5z = -17/5
y - 9z = -9
Therefore, the solution to the system is x = -17/5 + 1/5y + 3/5z, y = -9z + 9, and z is any real number.