Question 1144508
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<pre>
From the first equation, express b = 3a - 5c - 22 and substitute it into the second and the third equations. Then you will get


    4c = -12 - a - 2(3a - 5c - 22)    (2')    instead of the second equation, and

    2a - 19 = 6(3a - 5c -22) + 3c     (3')    instead of the third equation.


In this way, you just have the system of 2 equations (2') and (3') in 2 unknowns "a" and "c".


Write this system in the standard form


     7a -  6c =   32                  (4)

    16a - 27c =  113                  (5)


At this point, you have the system of 2 equations in 2 unknowns in the standard form.


I hope, that from this point your son will be able to complete the solution on his own.


If not, let me know.


<U>ANSWER</U>.  a= 2, b= -1, c= -3.
</pre>

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There is a bunch of lessons in this site on solving systems of linear equations in three unknowns by the Substitution and Elimination methods  

&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;&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=https://www.algebra.com/algebra/homework/Matrices-and-determiminant/OVERVIEW-of-LESSONS-on-solving-systems-in3-unknowns-by-Subst-and-Elim-methods.lesson>OVERVIEW of LESSONS on solving systems of linear equations in three unknowns by the Substitution and/or Elimination methods</A>


and by using determinants (Cramer's rule)

&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>



Also, &nbsp;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>" 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.