Solve the system. If there's no unique solution, label the system as either dependent or inconsistent.

2x + y + 3z = 12

x - y + 4z = 5

-4x + 4y - 16z = - 20

A. (4, 1, 2)

B. (1, 4, 2)

C. Inconsistent system (no solution)

D. Dependent system (infinite number of solutions)

simplify bottom equation by dividing all terms by 4 to get - x + y - 4z = - 5.

divide all terms by - 1 to get x - y + 4z = 5.

now you're only left with two equations since the bottom two are essentially the same.

solve for x in the second equation.

x = 5 + y - 4z

substitute x into the first equation and simplify.

2 (5 + y - 4z) + y + 3z = 12

10 + 2y - 8z + y + 3z = 12

3y - 5z = 2

substitute x into the second equation and solve for y.

5 + y - 4z - y