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

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Question 172787: Solve


system%28x-y%2B2z=-3%2C+x%2B2y%2B3z=4%2C+2x%2By%2Bz=-3%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations

system%28x-y%2B2z=-3%2C+x%2B2y%2B3z=4%2C+2x%2By%2Bz=-3%29


x-y%2B2z=-3 Start with the first equation


x=-3%2By-2z Add "y" to both sides. Subtract 2z from both sides. Now let's call this equation 4.


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2x%2By%2Bz=-3 Move onto the third equation


y=-3-2x-z Subtract 2x from both sides. Subtract "z" from both sides.


y=-3-2%28-3%2By-2z%29-z Plug in x=-3%2By-2z (equation 4).


y=-3%2B6-2y%2B4z-z Distribute


y=3-2y%2B3z Combine like terms.


y%2B2y=3%2B3z Add 2y to both sides.


3y=3%2B3z Combine like terms.


y=%283%2B3z%29%2F3 Divide both sides by 3 to isolate "y"


y=%283%29%2F3%2B%283z%29%2F3 Break up the fraction.


y=1%2Bz Reduce


y=z%2B1 Rearrange the terms. Let's call this equation 5.


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x%2B2y%2B3z=4 Now move onto the second equation


%28-3%2By-2z%29%2B2%28z%2B1%29%2B3z=4 Plug in x=-3%2By-2z (equation 4) and y=z%2B1 (equation 5)


-3%2By-2z%2B2z%2B2%2B3z=4 Distribute


-1%2By%2B3z=4 Combine like terms.


y%2B3z=4%2B1 Add 1 to both sides.


y%2B3z=5 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

x=-3%2By-2z Equation 4


y=z%2B1 Equation 5


y%2B3z=5 Equation 6



So let's solve the system of equations of 5 and 6
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y%2B3z=5 Start with equation 6


z%2B1%2B3z=5 Plug in y=z%2B1 (Equation 5).


1%2B4z=5 Combine like terms on the left side.


4z=5-1 Subtract 1 from both sides.


4z=4 Combine like terms on the right side.


z=%284%29%2F%284%29 Divide both sides by 4 to isolate z.


z=1 Reduce.

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y=z%2B1 Go back to Equation 5.


y=1%2B1 Plug in z=1


y=2 Add.

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x=-3%2By-2z Go back to equation 4.


x=-3%2B2-2%281%29 Plug in y=2 and z=1


x=-3%2B2-2 Multiply


x=-3 Combine like terms.



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Answer:


So the solutions are x=-3, y=2, and z=1

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