SOLUTION: solve: solutions of three equations in three variables: 2x+y-z=1 x+2y+2z=2 4x+5y+3z=3 PLEASE SHOW WORK!!! (IVE ASKED IN PREVIOUS QUESTIONS TO SHOW WORK AND NO ONE HAS

Question 798372: solve:
solutions of three equations in three variables:
2x+y-z=1
x+2y+2z=2
4x+5y+3z=3

PLEASE SHOW WORK!!! (IVE ASKED IN PREVIOUS QUESTIONS TO SHOW WORK AND NO ONE HAS DONE SO .. I JUST NEED TO UNDERSTAND HOW TO DO THIS!)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve:
solutions of three equations in three variables:
2x+y-z=1
x+2y+2z=2
4x+5y+3z=3
------------
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
----
6x+3y-3z=3 Eqn 1 times 3
4x+5y+3z=3 Eqn 3
-------------------------- Add
10x + 8y = 6 Eqn B
-------
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
------
It's obvious that the system is inconsistent.
--> no unique solution

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