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Question 187294: Solve the linear system with a single solution or using the addtion and substitution method.
14)2x-y+3z=14
x+y-2z=-5
3x+y- z=2
18) x-3y+2z=-11
2x-4y+3z=-15
3x-5y-4z=5''.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve each system in three variables
14)
2x-y+3z=14
x+y-2z=-5
3x+y- z=2
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Elimination and substitution is one way to do these.
1st, pick a variable to eliminate from 2 of the eqns. Since y has a coeff of 1 in all 3, it's the easiest.
Add eqn 3 to eqn 1, and then subtract it from eqn 2.
2x-y+3z=14
3x+y- z=2
-------------
5x+0y+2z = 16 Eqn A
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x+y-2z=-5
3x+y- z=2
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-2x+0y-z = -7 Eqn B
Now there are 2 eqns in x and z
Multiply Eqn A and B by something to get the same coeff for either x or z.
Multiply B by 2 to get 2z in both
5x+0y+2z = 16 Eqn A
-4x-2z = -14 Eqn B times 2
------------- Add these
x = 2
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Sub x into Eqn A, find z
z = 3
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Sub z and z into any eqn to find y
y = -2
------
x = 2
y = -1
z = 3
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Try this one. email me via the thank you note for help, or to check you work.
18)
x-3y+2z=-11
2x-4y+3z=-15
3x-5y-4z=5
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