Solve the system of equations. { x + 4 y − z = − 3 5 x − 6 y + z = − 16 − 5 x + 12 y − 3 z = 15 Find the correct choice below and, if necessary, fill in the answer boxes to complete your choice.A. There is one solution. The solution is (?,?,?).B. There are infinitely many solutions. The solution is ( x , y , z ) | x = ? , x = ? , y = ? , z is any real number .C. The solution is the empty set.

Question

Solve the system of equations.      {                            x          +          4          y          −          z          =          −          3                                      5          x          −          6          y          +          z          =          −          16                                      −          5          x          +          12          y          −          3          z          =          15                        Find the correct choice below and, if necessary, fill in the answer boxes to complete your choice.A. There is one solution. The solution is (?,?,?).B. There are infinitely many solutions. The solution is       (    x    ,    y    ,    z    )          |        x    =    ?    ,    x    =    ?    ,    y    =    ?    ,    z is any real number  .C. The solution is the empty set.

Irene Simon · Accepted Answer

Step 1Augmented matrix for given system of equations solution using Gauss-Jordan eliminationYour matrix                          X        1                    X        2                    X        3                    b                            1                    1                    4                    −        1                    −        3                            2                    5                    −        6                    1                    −        16                            3                    −        5                    12                    −        3                    15            Find the pivot in the 1st column in the 1st row                          X        1                    X        2                    X        3                    b                            1                              |                1                  |                            4                    −        1                    −        3                            2                    5                    −        6                    1                    −        16                            3                    −        5                    12                    −        3                    15            Eliminate the 1st column                          X        1                    X        2                    X        3                    b                            1                              |                1                  |                            4                    −        1                    −        3                            2                              |                0                  |                            −        26                    6                    −        1                            3                              |                0                  |                            32                    −        8                    0            Make the pivot in the 2nd column by dividing the 2nd row by -26                          X        1                    X        2                    X        3                    b                            1                    1                    4                    −        1                    −        3                            2                    0                              |                1                  |                            −        3                  /                13                    1                  /                26                            3                    0                    32                    −        8                    0            Eliminate the 2nd column                          X        1                    X        2                    X        3                    b                            1                    1                              |                0                  |                            −        1                  /                13                    −        41                  /                13                            2                    0                              |                1                  |                            −        3                  /                13                    1                  /                26                            3                    0                              |                0                  |                            −        8                  /                13                    −        16                  /                13            Make the pivot in the 3rd column by dividing the 3rd row by -8/13                          X        1                    X        2                    X        3                    b                            1                    1                    0                    −        1                  /                13                    −        41                  /                13                            2                    0                    1                    −        3                  /                13                    1                  /                26                            3                    0                    0                              |                1                  |                            2            Eliminate the 3rd column                          X        1                    X        2                    X        3                    b                            1                    1                    0                              |                0                  |                            −        3                            2                    0                    1                              |                0                  |                            1                  /                2                            3                    0                    0                              |                1                  |                            2            Step 2Solution set:  x  =  −  3  y  =  1      /    2  z  =  2(A) The solution is   (  −  3  ,  1      /    2  ,  2  )

Solve the system of equations.

Answered question

Answer & Explanation

New Questions in Pre-Algebra