Question

x-2y+3z=7, 2x+y+z=4 , -3x+2y-2z=-10 birinci dereceden 3 bilinmeyenli lineer denkleminin çözüm kümesini bulunuz.

Answer 1

x-2y+3z=7

2x+y+z=4

-3x+2y-2z=-10

x-2y+3z=7                      x-2y+3z=7              

-3x+2y-2z=-10             2(  2x+y+z=4)

-2x+0+z=-3                   5x+0+4z =15

-4(-2x+z=-3 )

5x+4z =15

13x+0=27

x= 27/13

-2x+0+z=-3  ==>  2x-z= 3  ==> 2(27/13) - 3 = z  ==> z= 15/13

2x+y+z=4 ==> 2(27/13) + y +15/13 = 4

                       y= -( 54 /13 +15/13) +4

  y= -69/13  +52/15  = -17/13 

{x,y,z} = {27/13,  -17/13 , 15/13}