Answer:x1 = 1, x2 = - 1, x3 = 3
Explanation:
x1 + 2x2 - x3 = - 4 - - - - - - - - - -1
x1 + 2x2 + x3 = 2 - - - - - - - - - -2
- x1 - x2 + 2x3 = 6 - - - - - - - - - -3
Let us eliminate x1 and x2. Subtracting equation 2 from equation 1, it becomes
-2x3 = - 6
x3 = -6/-2
x3 = 3
Adding equation 2 to equation 3, it becomes
x2 + 3x3 = 8 - - - - - - - - - - - 4
Substituting x3 = 3 into equation 4, it becomes
x2 + 3 × 3 = 8
x2 + 9 = 8
x2 = 8 - 9 = -1
Substituting x2 = -1 and x3 = 3 into equation 2, it becomes
x1 + 2 × -1 + 3 = 2
x1 - 2 + 3 = 2
x1 + 1 = 2
x1 = 2 - 1 = 1
Let us check by substituting x1 = 1, x2 = -1 and x3 = 3 into equation 1. It becomes
1 + 2 × - 1 - 3 = - 4
1 - 2 - 3 = - 4
-1 - 3 = - 4
-4 = - 4