Solve the system, show each step. x + y + z = -4 -x + 2y + 3z = 3 x - 4y - 2z = -15

The solution of the system of equations is , and .

Explanation:

The given equations are,

           ..... (1)

        ..... (2)

       ...... (3)

From equation we get,

Put this value in equation (4) and (5).

    .... (4)

 .....(5)

Use elimination method to solve the equations (4) and (5).

Multiply equation (4) by 3 and equation (5) by 4, then add both equations as shown in figure,

Put this value in equation (4).

Put and in equation (1).

Therefore, the The solution of the system of equations is , and .

The given equations are

x + y + z = -4

-x + 2 y + 3 z = 3

x - 4 y - 2 z = -15

Writing in matrix form

A=   1     1      1             X=   x       B=   -4

     -1     2     3                    y               3            ⇒A,X,B are in matrix form.

       1     -4    -2                   z              -15

i.e  Ax=B

x =B

but ,=Adj.(A)/Determinant A

Determinant of A= 1(-4+12) -1(2-3)+1(4-2)=8+1+2=11

To find Adjoint of matrix A, we will find the cofactor of A and then it's transpose.

=-4+12=8,

Now taking cofactor, and getting the adjoint

Adjoint (A)= 8     -2       1

                     1      - 3       -4

                     2       5         3

Adjoint(A). B=  -53

                        47

                         -38

=   -53/11

                                                                                        47/11

                                                                                         -38/11

So, solution set is , x=-53/11, y=47/11, z=-38/11

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