Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.