Answered

IDNLearn.com: Your trusted source for finding accurate and reliable answers. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

Solve the following three variable system.

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

Sagot :

Kate200468idn
[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]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.