SOLUTION: I need help solving this linear equation in three variables 5y -7z = 14 2x + y + 4z = 10 2x + 6y - 3z = 30 please help me solve this equation.\ thanks megan

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Question 153589: I need help solving this linear equation in three variables
5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
please help me solve this equation.\
thanks
megan
Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
I need help solving this linear equation in three variables
5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
please help me solve this equation.
thanks
megan

There is no solution.  This is what is called an inconsistent
system.

There are many methods to solve a system of three equations
in three unknowns. If you will re-post telling which method
you are studying, then we can use that method and show how 
you can tell that there is no solution.

Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
0x + 5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
-------------------------
Switch line 1 and line 2 to get:
-------------------------
2x + y + 4z = 10
0x + 5y -7z = 14
2x + 6y - 3z = 30
-------------------------
Subtract line 1 from line 3:
2x + y + 4z = 10
0x + 5y -7z = 14
0x + 5y -7z = 20
-------------------------
2x + y + 4z = 10
0x + 5y -7z = 14
0x + 0y -0z = 6
------------------------
The 3rd line is a contradiction and indicates there is no
solution to the system of three equations.
===========================
Cheers,
Stan H.