Solve System Of Equations

Question

I have a question on how to simplify this system of equations. If a free variable is needed please use the parameter t.

 

4x-y+z=6

2y+6z=36

x+z=6

 

Thank you!

Answer 1

Rearrange:       x          + z = 6

                            2y + 6z = 36

                     4x -  y +   z  = 6

 

Multiply equation 1 by -4 and add to equation 3:

 

                      x           + z = 6

                            2y + 6z = 36

                            -y  - 3z  = -18

 

Multiply equation 2 by 1/2 and add to equation 3:

 

                      x           + z = 6

                            2y  + 6z = 36

                                      0 = 0

 

So, x = 6 - z

     y = 18 - 3z

     z = any real number, t

 

Solution set:  {(6-t, 18-3t, t) l t = any real number}

 

                  = {t(-1, -3, 1) + (6, 18, 0) l t = any real number}