Final answer:
To reduce the given system of equations to upper triangular form, perform row operations to eliminate variables. Then, solve the system using back substitution.
Step-by-step explanation:
To reduce the given system of equations to upper triangular form, we can use row operations. In this case, we can start by multiplying the first equation by -2 and adding it to the second equation, which eliminates the x variable in the second equation. Next, we can multiply the first equation by 1 and adding it to the third equation, which eliminates the x variable in the third equation. The resulting system of equations in upper triangular form is:
2x + 3y + z = 8
0y + y + 3z = 16
0y + 0y + (-1)z = -8
The pivots in this system are 2, 1, and -1. To solve by back substitution, we start with the last equation and find z = -8/(-1) = 8. Then, substitute this value of z into the second equation to find y: y + 3(-8) = 16, y - 24 = 16, y = 40. Finally, substitute the values of y and z into the first equation to find x: 2x + 3(40) + 8 = 8, 2x + 120 + 8 = 8, 2x = -120, x = -60.