(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.