Question 1162557
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<pre>

     x +  y +  z = 17     (1)

    2x + 3y + 4z = 49     (2)

    3x -  y      = 21     (3)


It can be solved by the Substitution method, or by the Elimination method, or by using determinants (the Cramer's rule).


To simplify the life, I will use one of the free of charge online solvers

https://matrix.reshish.com/cramSolution.php

(Cramer's rule).


The answer is  x = 8,  y = 3,  z = 6.
</pre>

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If you wish to learn about the methods of solution, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-3-unknowns-by-the-Substitution-method.lesson>Solving systems of linear equations in 3 unknowns by the Substitution method</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/BRIEFLY-on-solving-systems-of-linear-eqns-in-3-unknowns-by-the-Subst-method.lesson>BRIEFLY on solving systems of linear equations in 3 unknowns by the Substitution method</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-3-unknowns-by-the-Elimination-method.lesson>Solving systems of linear equations in 3 unknowns by the Elimination method</A> &nbsp;and

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/BRIEFLY-on-solving-systems-of-linear-eqns-in-3-unknowns-by-the-Eliminat-method.lesson>BRIEFLY on solving systems of linear equations in 3 unknowns by the Elimination method</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Determinant-of-a-3x3-matrix.lesson>Determinant of a 3x3 matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Co-factoring-a-3x3-determinant.lesson>Co-factoring the determinant of a 3x3 matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/HOW-TO-solve-system-of-linear-eqns-in-three-unknowns-using-det.lesson>HOW TO solve system of linear equations in three unknowns using determinant (Cramer's rule)</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-three-unknowns-using-determinant.lesson>Solving systems of linear equations in three unknowns using determinant (Cramer's rule)</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-word-problems-by-reducing-them-to-systems-of-linear-equations-in-three-unknowns.lesson>Solving word problems by reducing to systems of linear equations in three unknowns</A>

in this site.



Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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



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

<A HREF=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</A>


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