a) 2.x - 6.y + z = 30
b) -x + 3.y +2.z = - 20
c) -6.x -5.y +6.z = 7
1st, let's take a) and b) alone and let's eliminate x
a) 2.x - 6.y + z = 30
b) -x + 3.y +2.z = - 20
2nd) multiply b) with 2 and once done add a) with the result of b):
b') times 2 → -2.x+6.y+4.z = - 40. Now add it to a):
a) 2.x - 6.y + z = 30
b') -2.x+6.y+4.z = - 40
+ ----------------- -----
0.x + 0.y + 5.z = -10 → z = -2
Now replace z with its value (-2) in :
b) -x + 3.y +2.z = - 20 → - x + 3.y -4 = -20 → - x +3.y = -16
c) -6.x -5.y +6.z = 7 → -6.x - 5.y -12 = 7 → - 6.x -5.y = 19
Consider the result of:
- x +3.y = -16 and
- 6.x -5.y = 19
Now let's eliminate x from both equations.
To that end multiply the 1st one by (-6)
6x - 18y = 96 and add it to - 6.x -5.y = 19
6x - 18y = 96
-6.x -5.y = 19
+--------- ----
0.x - 23.y 115 → 23y = -115 and y = -115/23 = - 5→→ y = -5
Now that you have the value of z= - 2 and y = -5, plugin in any of the equation and you will find x = 1. So the final result is:
x = 1 ; y = - 5 ; and z = - 2
