SOLUTION: hello, we are working with linear equations. i am trying to solve 3 equations with 3 variables each x,y, and z but the substitution method is not working for me. here are equations
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Question 358078: hello, we are working with linear equations. i am trying to solve 3 equations with 3 variables each x,y, and z but the substitution method is not working for me. here are equations:
x - y + 3z = 8
3x + y - 2z = -2
2x + 4y + z = 0
I don't really want answers i need to see how. thank you Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! There's more than one way. I'll use elimination.
Look for coefficients that make it easiest to eliminate one of the 3 variables.
x - y + 3z = 8
3x + y - 2z = -2
2x + 4y + z = 0
-----------
1*y is in the 1st and 2nd, so eliminate it first
x - y + 3z = 8
3x + y - 2z = -2
------------------ Add
4x + z = 6
Multiply eqn 1 by 4
4x - 4y +12z = 32
2x + 4y + z = 0
----------------- Add
6x + 13z = 32
Now the x's can be eliminated
Multiply 4x + z = 6 by 3 and the other by 2
12x + 3z = 18
12x +26z = 64
-------------- Subtract
-23z = -46
z = 2
------
Sub for z in 4x + z = 6
--> x = 1
-----------
Sub for x and z in one of the original eqns to find y.
