SOLUTION: SYSTEM OF 3 EQUATIONS WITH 3 UNKNOWNS FIND THE SOLUTION SET FOR THE FOLLOWING SYSTEM OF EQUATIONS: 4X -2Y -3Z = 8 5X +3Y -4Z = 4 6X -4Y -5Z = 12

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Question 208208: SYSTEM OF 3 EQUATIONS WITH 3 UNKNOWNS

FIND THE SOLUTION SET FOR THE FOLLOWING SYSTEM OF EQUATIONS:
4X -2Y -3Z = 8
5X +3Y -4Z = 4
6X -4Y -5Z = 12
Answer by pjalgeb(9) (Show Source):
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REQUIRED: Find the solution set {(x, y z)} for the system given.
SOLUTION:
The augmented 3x3 matrix for the above system of equations is:
| 4 -2 -3 | 8 |
| 5 3 -4 | 4 |
| 6 -4 -5 | 12 |
By Cramers Rule:

First, lets solve for D, Dx, Dy and Dz:

D = | 4 -2 -3 |
| 5 3 -4 |
| 6 -4 -5 |
D = 4(-15-16) -5(10-12) +6(8+9)
D = 4(-31) -5(-2)+ 6(17)
D = -124 +10 +102
D = -124 -112

Dx = | 8 -2 -3 |
| 4 3 -4 |
| 12 -4 -5 |
Dx = 8(-15-16) -4(10-12) + 12(8+9)
Dx = 8(-31) -4(-2) + 12(17)
Dx = -248 +8 + 204
Dx = -248 +212

Dy = | 4 8 -3 |
| 5 4 -4 |
| 6 12 -5 |

Dy = 4(-20+48) -5(-40+36) +6(-32+12)
Dy = 4(28) -5(-4) +6(-20)
Dy = 112 +20 -120
Dy = 132 -120

Dz = | 4 -2 8 |
| 5 3 4 |
| 6 -4 12 |
Dz = 4(36+16) -5(-24+32) +6(-8-24)
Dz = 4(52) -5(8) +6(-32)
Dz = 208 -40 -192
Dz = 168 -192

Answer: The solution set is {(3,-1,2)}