mathcalculus
HELP! how to solve system of equations
x-2y+z=-1
y+2z=-4
x+y+3z=-5
what do we do when there is a missing variable??? :(
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woody84
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what are you solving for??
mathcalculus
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x,y, and z
mathcalculus
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I'm not sure what to do since the x is missing.
Directrix
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Write the system as:
x - 2y +z =-1
0x +y+ 2z=-4
x + y + 3z = -5
In the first and third equations, eliminate the variable x.
Then, you will have a system of 2 by 2 equations in the unknowns y and z.
Of those two equations, eliminate a variable and solve for the other.
If you are allowed to use technology, take a look at the online 3 x 3 linear equation system solver at:
http://math.bd.psu.edu/~jpp4/finitemath/3x3solver.html
@mathcalculus
Directrix
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Question?
mathcalculus
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thank you
mathcalculus
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im trying to solve it step by step
Directrix
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x - 2y +z =-1
0x +y+ 2z=-4
x + y + 3z = -5
x - 2y +z =-1 x - 2y +z =-1
x + y + 3z = -5 --multiply through by -1 -> -x - y - 3z = 5
----------------
-3y - 2z = 4
mathcalculus
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ok
mathcalculus
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i got a little lost. now i know why
mathcalculus
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i got that, so what about the second equation?
Directrix
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@mathcalculus
Your Task:
Solve this system - Just add them.
-3y - 2z = 4
y+ 2z=-4
-----------------
mathcalculus
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it bothers me that the 0x is there.
Directrix
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Don't look at it.
When I eliminated the "x" in equations #1 and #3, the 0x was not an issue.
mathcalculus
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i got this: -2y=0
mathcalculus
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but it can't be. it's undefined.
Directrix
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Note that here:
Solve this system - Just add them.
-3y - 2z = 4
y+ 2z=-4
-----------------
I excluded the 0x term. It is just a placeholder of sorts.
mathcalculus
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0/2?
mathcalculus
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yeah i know.
Directrix
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-2y = 0
y= 0/2
y = 0-->
You have division by 0 and division into 0 mixed up.
mathcalculus
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so y is 0?
mathcalculus
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okay i got that step right.
mathcalculus
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z=2
mathcalculus
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x=-6
mathcalculus
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it's wrong... :(
Directrix
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It is wrong. But, unless you show your steps, I cannot help you find the error.
mathcalculus
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z=-2
mathcalculus
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ok hold on.
mathcalculus
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i got it right! x=1 y=0 z=-2 ! =]
mathcalculus
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thanks so much! i really aprreciate it!
Directrix
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You are welcome.