SOLUTION: Solve the following system of linear equations with three unknowns. (Note: Answers are in order of A,B,C.) 2A+2B+3C=15 A-B+C=2 3A-2B+2C=5 .. I'm stuck on this on some hom

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Question 227569: Solve the following system of linear equations with three unknowns.
(Note: Answers are in order of A,B,C.)
2A+2B+3C=15
A-B+C=2
3A-2B+2C=5
.. I'm stuck on this on some homework and it would be awesome if you could let me know how to do this.
Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
adding the 1st and 3rd eqns ___ 5A + 5C = 20 ___ A + C = 4 ___ A = 4 - C

substituting into 2nd eqn ___ 4 - B = 2 ___ 2 = B

substituting into 1st eqn ___ 2(4 - C) + 2(2) + 3C = 15 ___ 8 - 2C + 4 + 3C = 15 ___ 12 + C = 15 ___ C = 3

substituting ___ A = 4 - (3) = 1
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Solve the following system of linear equations with three unknowns.
(Note: Answers are in order of A,B,C.)
2A+2B+3C=15
A-B+C=2
3A-2B+2C=5
.. I'm stuck on this on some homework and it would be awesome if you could let me know how to do this. 

There are many ways to solve systems of equations:

1. Substitution only 
2. Elimination (addition) only
3. Substitution and elimination (addition)
4. Cramer's rule (determinants)
5. Augmented matrix method with partial pivoting 
6. Gauss-Jordan method with complete pivoting
7. The AX=B method (inverse matrix method)

If you will tell us which method you are studying,
then I can help you, but otherwise all I can do
is give you the solution, which any of the 7 methods
above will give, namely

(x,y,z) = (1,2,3)

Edwin
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