SOLUTION: Solve the following system. 2x + 4y + 3z = 2 x + 2y - z = 0 4x + y - z = 6

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Question 1043287: Solve the following system.
2x + 4y + 3z = 2
x + 2y - z = 0
4x + y - z = 6
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve the following system.
2x + 4y + 3z = 2
x + 2y - z = 0
4x + y - z = 6
~~~~~~~~~~~~~~~~~~~~ 

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?

My lessons in this site on solving systems of linear equations in three unknowns by the Substitution and the Elimination methods are
    - Solving systems of linear equations in 3 unknowns by the Substitution method,
    - BRIEFLY on solving systems of linear equations in 3 unknowns by the Substitution method,
    - Solving systems of linear equations in 3 unknowns by the Elimination method  and
    - BRIEFLY on solving systems of linear equations in 3 unknowns by the Elimination method

My lessons in this site on solving systems of two linear equations in two unknowns are
    - Solution of a linear system of two equations in two unknowns by the Substitution method
    - Solution of a linear system of two equations in two unknowns by the Elimination method
    - Solution of a linear system of two equations in two unknowns using determinant
    - Geometric interpretation of a linear system of two equations in two unknowns
    - Solving word problems using linear systems of two equations in two unknowns