Question

How do you sovle this system of linear equations:

4x-y+z=6

2y+6z=36

x+z=6

Answer 1

System of linear equations:

4x - y + z  =  6  -------------------->  (!)

2y + 6z  =  36 ------------------> (2)

x + z  =  6 ---------------------------> (3)

Multiply Eq (3) with 4 and Subtract  Eq (1) from it

Eq (3) X 4  =====>   4x + 0y + 4z  =  24

Eq (1)  ========>   4x -   y   + z   =  6

                                      (-)     (+)     (-)         (-)

                                  --------------------------------------

                                          y + 3z  =  18 ---------------> (4)

Multiply Eq (4) with 2 and compare it with Eq (2)

Eq (2)  ==========>  2y + 6z  =  36

Eq (4) X 2  =======>  2y + 6z  =  36

Above two lines are coinciding each other

Hence it has infinitely many solutions.

Answer :

The System of equations has infinitely many solutions.