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I got x₁=5/2
x₂=6
x₃=t (free variable)
The answer says I am wrong. Care to tell me what I did wrong?

x_3=0

Right. But whats wrong with my other answers?

Here is what the online page looks like:

Shouldn't the other variables be in terms of the free variable?

What did were your elimination steps?

but t is a free variable is it not? SO it can be any value it wants.

Did you solve it like this?

No... How did you get 0,0 and 1?

I just added in the equation \(x_3=t\)

Sorry, that doesn't make sense.

I added in the equation: \[
0x_1+ 0x_2 +1x_3 = t
\]

Ohh I see.

All of the elimination you did before should work for the most part.

So I do a back substitution?

You first want to get the second row to have a zero in it's first colum

because x3=t so solve the others n terms of t.

then you can back substitute

1 second.

x₁=2.5+3.5t ?

x₂=6-2t?

yeah I'm getting that too

did you try it?

One attempt left :3 . Fingers crossed.

you can double check it you know

How?

plug in each equation into the equations

Assign a random number to t and see if it works?

like, plug in t for x_3 and 6-2t for x_2 into the equations

hmm actually I'm not quite sure how to double check it

let me look at wolfram

You can do this on wolfram? O_O .

http://www.wolframalpha.com/input/?i=2x%2B5y%2B3z%3D35%2C+12x%2B31y%2B20z%3D216%2C+z+%3D+t

wolfram agrees... it's just a matter of the stupid answer verify thing not being a wingspan

THANKS!!! It's right :) .

No problem. Matrix is your friend.

I love Linear algebra <3 .