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Solve the following three variable system.

2x + 3y + 4z = 9
-x + 2y - z = 0
-2x + 4y + z = 3

Sagot :

kate200468
[tex]1)\ \ \ 2x + 3y + 4z = 9\\2)\ \ \ -x + 2y - z = 0\\3)\ \ \ -2x + 4y + z = 3\\===================================\\3)\ \ \ -2x + 4y + z = 3\ \ \ \Rightarrow\ \ \ z=2x-4y+3\\\\1)\ \ \ 2x + 3y + 4z = 9\ \ \ \Rightarrow\ \ \ 2x + 3y + 4(2x-4y+3) = 9\\2x+3y+8x-16y+12=9\\10x-13y=-3\\\\2)\ \ \ -x + 2y - z = 0\ \ \ \Rightarrow\ \ \ -x+2y-(2x-4y+3)=0\\-x+2y-2x+4y-3=0\\-3x+6y=3\ /:(-3)\\x-2y=-1\ \ \ \Rightarrow\ \ \ x=2y-1\\\\[/tex]

[tex]1)\ \ \ 10x-13y=-3 \ \ \ \Rightarrow\ \ \ 10(2y-1)-13y=-3\\20y-10-13y=-3\\7y=7\ /:7\ \ \ \Rightarrow\ \ \ y=1\\\\2)\ \ \ x=2y-1\ \ \ \Rightarrow\ \ \ x=2\cdot2-1=1\\\\3)\ \ \ z=2x-4y+3\ \ \ \Rightarrow\ \ \ z=2\cdot1-4\cdot1+3=2-4+3=1\\\\Ans.\ x=y=z=1[/tex]
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