Question 798372
solve: 
solutions of three equations in three variables: 
2x+y-z=1
x+2y+2z=2
4x+5y+3z=3 
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Pick a variable to eliminate
z first.
4x+2y-2z =2 Eqn 1 times 2
x+2y+2z = 2 Eqn 2
----------------------- Add
5x + 4y = 4  Eqn A
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6x+3y-3z=3 Eqn 1 times 3
4x+5y+3z=3 Eqn 3
-------------------------- Add
10x + 8y = 6  Eqn B
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Now you have 2 eqns in 2 variables.
The next step is to eliminate x or y.
5x + 4y = 4  Eqn A
5x + 4y = 3  Eqn B times 1/2
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It's obvious that the system is inconsistent.
--> no unique solution