SOLUTION: 2x-3y+7z=-1,3x+z=6,x+2y-2z=-1

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Question 1073996: 2x-3y+7z=-1,3x+z=6,x+2y-2z=-1
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use Cramer's rule,
A=%28matrix%283%2C3%2C%0D%0A2%2C-3%2C7%2C%0D%0A3%2C0%2C1%2C%0D%0A1%2C2%2C-2%29%29
abs%28A%29=17
.
.
.
A%5Bx%5D=%28matrix%283%2C3%2C%0D%0A-1%2C-3%2C7%2C%0D%0A6%2C0%2C1%2C%0D%0A-1%2C2%2C-2%29%29
abs%28A%5Bx%5D%29=53
.
.
.
A%5By%5D=%28matrix%283%2C3%2C%0D%0A2%2C-1%2C7%2C%0D%0A3%2C6%2C1%2C%0D%0A1%2C-1%2C-2%29%29
abs%28A%5By%5D%29=-92
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.
.
A%5Bz%5D=%28matrix%283%2C3%2C%0D%0A2%2C-3%2C-1%2C%0D%0A3%2C0%2C6%2C%0D%0A1%2C2%2C-1%29%29
abs%28A%5Bz%5D%29=-57
.
.
.So,
x=abs%28A%5Bx%5D%29%2Fabs%28A%29=53%2F17
.
.
y=abs%28A%5By%5D%29%2Fabs%28A%29=-92%2F17
.
.
z=abs%28A%5Bz%5D%29%2Fabs%28A%29=-57%2F17
.
.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
On the Cramer's rule for solving systems of 3 equations in 3 unknowns see the lesson
    - HOW TO solve system of linear equations in three unknowns using determinant (Cramer's rule)
    - Solving systems of linear equations in three unknowns using determinant (Cramer's rule)
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
     "3x3-Matrices, determinants, Cramer's rule for systems in three unknowns"


In addition, there are many free of charge SOLVERS on a Cramer's rule in the internet.

One of such popular solvers is in this site under the link
https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver

https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver