Answer:
Explanation:
Given the system of equation
3x1 − 2x2 + x3 = −10 ............. 1
2x1 + 6x2 − 4x3 = −10 ............ 2
−8x1 − 2x2 + 5x3 = −26 ............... 3
Reduce the system of equations:
multiply equation 1 by 3 and add to 2
Eqn 1 * 3 gives;
9x1 − 6x2 + 3x3 = −30
Add to equation 2:
9x1+2x1 +(3x3-4x3) = -30-10
11x1 - x3 = -40 ........... 4
multiply eqn 3 by 3 and add to eqn 2
eqn 3 * 3 gives
−24x1 − 6x2 + 15x3 = − 78
Add to eqn 2:
-24x1+2x1)+15x3-4x3 = -78-10
-22x1 + 11x3 = -88 ......... 5
solve 4 and 5:
11x1 - x3 = -40 ........... 4 * 2
-22x1 + 11x3 = -88 ......... 5 * 1
.....................................................
22x1 - 2x3 = -80
-22x1 + 11x3 = -88
Add together:
-2x3 + 11x3 = -80-88
9x3 = -168
x3 = -168/9
x3 = 18.7
subtitute x3 = 18.7 into 4
11x1 - 18.7 = -40
11x1 = -40+18.7
11x1 = -21.3
x1 = -21.3/11
x1 = -1.93
Substitute x1 and x3 into 1
3(-1.93)− 2x2 + 18.7 = −10
- 5.79-2x2 = -28.7
-2x2 = -18.7 +5.79
-2x2 = -22.91
x2 = 11.455