Question 1043287
.
Solve the following system.
2x + 4y + 3z = 2 
x + 2y - z = 0 
4x + y - z = 6
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<pre>
2x + 4y + 3z = 2    (1)
 x + 2y -  z = 0    (2)
4x +  y -  z = 6    (3)


Multiply equation (2) by 2. You will get

2x + 4y - 2z = 0.    (2')

Now distract eqn.(2') from eqn.(1). You will get

5z = 2.   Hence,  z = 0.4.

Thus we just found the unknown z. It is known now.

Next, substitute this value of z into equations 2) and (3). You will get

x + 2y = 0.4,        (4)
4x + y = 6.4.        (5)

So, we reduced the original 3x3 system to 2x2-system.

At this point, I think that if you got an assignment to solve the system in 3 unknowns, you easily can solve the system in 2 unknowns.

Can you complete the solution on your own?
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My lessons in this site on solving systems of linear equations in three unknowns by the Substitution and the Elimination methods are 

&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>


My lessons in this site on solving systems of two linear equations in two unknowns are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-system-of-two-eqns-by-the-Subst-method.lesson>Solution of a linear system of two equations in two unknowns by the Substitution method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of a linear system of two equations in two unknowns by the Elimination method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of a linear system of two equations in two unknowns using determinant</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of a linear system of two equations in two unknowns</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solving-word-probs-using-linear-systems-of-two-eqns-with-two-unknowns.lesson>Solving word problems using linear systems of two equations in two unknowns</A>