- #1
themadhatter1
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Homework Statement
Solve for a, b, and c.
4c+6b+14a=25
6c+14b+36a=21
14c+36b+98a=105
Homework Equations
The Attempt at a Solution
I need to solve this without using matrices.
The easiest way would be to get it into row echelon form and back-substitute. However, I'm not sure how you can get this system of equations into row echelon form.
I can subtract 6 times the first equation from the third equation:
14c+36b+48a=105
- 24c+36b+84a=150
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-10c+0b+14a=-45
so you get:
-10c+0b+14a=-45
6c+14b+36a=21
14c+36b+98a=105
Next the only thing you could do would be subtract 7 times the first equation from the third equation, but if you did that you would be getting rid of the a term but reintroducing the b term which I just eliminated.
How do you get this into Row Echelon form to solve?