SOLUTION: Solve {{{system(x-y+2z=-3, x+2y+3z=4, 2x+y+z=-3)}}}

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Question 172787: Solve



Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given system of equations




Start with the first equation


Add "y" to both sides. Subtract from both sides. Now let's call this equation 4.


-------------------------------

Move onto the third equation


Subtract 2x from both sides. Subtract "z" from both sides.


Plug in (equation 4).


Distribute


Combine like terms.


Add 2y to both sides.


Combine like terms.


Divide both sides by 3 to isolate "y"


Break up the fraction.


Reduce


Rearrange the terms. Let's call this equation 5.


-------------------------------

Now move onto the second equation


Plug in (equation 4) and (equation 5)


Distribute


Combine like terms.


Add 1 to both sides.


Add. Now let's call this equation 6.


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Are you with me so far? Well after all that substitution and simplification, we have the equations

Equation 4


Equation 5


Equation 6



So let's solve the system of equations of 5 and 6
--------------------------------------------------

Start with equation 6


Plug in (Equation 5).


Combine like terms on the left side.


Subtract from both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.

---------------------------------------------------

Go back to Equation 5.


Plug in


Add.

---------------------------------------------------

Go back to equation 4.


Plug in and


Multiply


Combine like terms.



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Answer:


So the solutions are , , and

These solutions form the ordered triple (-3,2,1)

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