solve the equation using cramer's rule

Question

       (i)  x + y + 2z = 0                                 (ii)  x-y + z = 2

       -3x – y + 2z – 1 = 0                                x + 2y + 3z = 6

       x + 2y – z + 4 = 0                                   x – 3y- z = -4

Answer 1

(i)  x + y + 2z = 0         |  1  1  2 |            (ii)  x - y + z = 2            | 1 -1  1 |

  -3x – y + 2z = 1  D = | -3 -1  2 | = -14        x + 2y + 3z = 6  D= | 1  2  3 | = -2

     x + 2y – z = -4        |  1  2 -1 |                 x – 3y- z = -4           | 1 -3 -1 |

Dx	Dy	Dz	Dx	Dy	Dz
|  0  1  2 | |  1 -1  2 | | -4  2 -1 |	|  1  0  2 | | -3  1  2 | |  1 -4 -1 |	|  1  1  0 | | -3 -1  1 | |  1  2 -4 |	|  2 -1  1 | |  6  2  3 | | -4 -3 -1 |	| 1  2  1 | | 1  6  3 | | 1 -4 -1 |	| 1 -1  2 | | 1  2  6 | | 1 -3 -4 |
-7-4=-11	7+22=29	2-11=-9	14+6-10=10	6+8-10=4	10-10-10=-10
x=-11/-14=11/14	y=-29/14	z=-9/-14=9/14	x=-5	y=-2	z=5

CHECK

(i) (11/14,-29/14,9/14):

11/14-29/14+18/14=0 OK;

-33/14+29/14+18/14-1=14/14-1=0 OK;

11/14-58/14-9/14+4=-56/14+4=0 OK.

(ii) (-5,-2,5)

-5+2+5=2 OK;

-5-4+15=6 OK;

-5+6-5=-4 OK.