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??? :(

- anonymous

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- anonymous

what are you solving for??

- anonymous

x,y, and z

- anonymous

I'm not sure what to do since the x is missing.

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- Directrix

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

Question?

- anonymous

thank you

- anonymous

im trying to solve it step by step

- Directrix

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

- anonymous

ok

- anonymous

i got a little lost. now i know why

- anonymous

i got that, so what about the second equation?

- Directrix

@mathcalculus
Your Task:
Solve this system - Just add them.
-3y - 2z = 4
y+ 2z=-4
-----------------

- anonymous

it bothers me that the 0x is there.

- Directrix

Don't look at it.
When I eliminated the "x" in equations #1 and #3, the 0x was not an issue.

- anonymous

i got this: -2y=0

- anonymous

but it can't be. it's undefined.

- Directrix

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.

- anonymous

0/2?

- anonymous

yeah i know.

- Directrix

-2y = 0
y= 0/2
y = 0-->
You have division by 0 and division into 0 mixed up.

- anonymous

so y is 0?

- anonymous

okay i got that step right.

- anonymous

z=2

- anonymous

x=-6

- anonymous

it's wrong... :(

- Directrix

It is wrong. But, unless you show your steps, I cannot help you find the error.

- anonymous

z=-2

- anonymous

ok hold on.

- anonymous

i got it right! x=1 y=0 z=-2 ! =]

- anonymous

thanks so much! i really aprreciate it!

- Directrix

You are welcome.

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