Question

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 – 4z = –20

A. Dependent system (infinite number of solutions)
B. Inconsistent system (no solution)
C. (4, 1, 2)
D. (1, 4, 2)

Answer 1

Neither c or d are correct for the entire system so it has to be B. A is not possible because we have already proved two solutions to be incorrect

Answer 2

Answer:

The solution of the equations are

     $x=\frac{17}{3},y=\frac{2}{3}\texttt{ and }z=0$

So all the options are wrong.

Step-by-step explanation:

We have

    2x + y + 3z = 12 -------------------eqn 1

    x – y + 4z = 5 -------------------eqn 2

    –4x + 4y – 4z = –20 -------------------eqn 3

eqn 2 x 2

   2x – 2y + 8z = 10 -------------------eqn 4

eqn 4 - eqn 1

   2x – 2y + 8z - (2x + y + 3z) = 10 - 12

   -3y +5z = -2 -------------------eqn 5

eqn 1 x 2

    4x + 2y + 6z = 24 -------------------eqn 6

eqn 3 + eqn 6

      –4x + 4y – 4z + 4x + 2y + 6z = -20 + 24

       6y + 2 z = 4 -------------------eqn 7

eqn 5 x 2

      -6y +10z = -4 -------------------eqn 8

eqn 7 + eqn 8

      12 z = 0

       z = 0

Substituting in eqn 7

        6y + 0 = 4

         $y=\frac{2}{3}$

Substituting in eqn 2

       $x-\frac{2}{3}+4\times 0=5\\x=\frac{17}{3}$

So the solution of the equations are

     $x=\frac{17}{3},y=\frac{2}{3}\texttt{ and }z=0$

So all the options are wrong.