SOLUTION: Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 Pls pro

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 Pls pro      Log On


   

Question 1075270: Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
Pls provide step by step answer
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Add R1 and R2,
x%2By%2Bz%2Bx-y%2B3z=-5-1
2x%2B4z=-6
R4:x%2B2z=-3
Add R2 and R3,
x-y%2B3z%2B4x%2By%2Bz=-1-2
R5:5x%2B4z=-3
Multiply R4 by -5 and add to R5,
-5x-10z%2B5x%2B4z=15-3
-6z=12
z=-2
So then working backwards,
x%2B2%28-2%29=-3
x-4=-3
x=1
and
1%2By-2=-5
y=-4