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)

The solution of the equations are

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

Substituting in eqn 2

So the solution of the equations are

So all the options are wrong.

10% of increase is the final answer! : )

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