SOLUTION: solve each system of linear equations with 3 variables and write the answers as an ordered triple, (x,y,z). SHOW HOW PLEASE. 3x+2y+4z=9 2x-2y+z=1 -x+3x-z=1

Algebra ->  Trigonometry-basics -> SOLUTION: solve each system of linear equations with 3 variables and write the answers as an ordered triple, (x,y,z). SHOW HOW PLEASE. 3x+2y+4z=9 2x-2y+z=1 -x+3x-z=1       Log On


   

Question 1074634: solve each system of linear equations with 3 variables and write the answers as an ordered triple, (x,y,z). SHOW HOW PLEASE.
3x+2y+4z=9
2x-2y+z=1
-x+3x-z=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%0A3%2C2%2C4%2C%0D%0A2%2C-2%2C1%2C%0D%0A-1%2C3%2C-1%29%29
abs%28A%29=15
.
.
.
A%5Bx%5D=%28matrix%283%2C3%2C%0D%0A9%2C2%2C4%2C%0D%0A1%2C-2%2C1%2C%0D%0A1%2C3%2C-1%29%29
abs%28A%5Bx%5D%29=15
.
.
.
A%5By%5D=%28matrix%283%2C3%2C%0D%0A3%2C9%2C4%2C%0D%0A2%2C1%2C1%2C%0D%0A-1%2C1%2C-1%29%29
abs%28A%5By%5D%29=15
.
.
.
A%5Bz%5D=%28matrix%283%2C3%2C%0D%0A3%2C2%2C9%2C%0D%0A2%2C-2%2C1%2C%0D%0A-1%2C3%2C1%29%29
abs%28A%5Bz%5D%29=15
.
.
.
So,
x=abs%28A%5Bx%5D%29%2Fabs%28A%29=15%2F15=1
.
.
y=abs%28A%5By%5D%29%2Fabs%28A%29=15%2F15=1
.
.
z=abs%28A%5Bz%5D%29%2Fabs%28A%29=15%2F15=1
.
.

Answer by ikleyn(52794) 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