Not solvable system of linear equations in Mathematica

How can I find for system of linear equations, that the system would not be solvable?

I tryed with this code:

Code:

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x = 10
y = 10
z = 10
Solve[{ 9 x - 8 y + t*z == 1, 6 x - 8 y - 5 z == 1,  3 x  -7 y + 9 z == 1}, {t}]

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You have a highly over-determined system there. There are no solutions. Think about it:

90-80+10t=1
60-80-50=1
30-70+90=1

Some of those equations are downright incorrect. I would review your steps for arriving at that system of equations. What's the bigger context for this problem?

Sorry, forget x,y,z values.

I need to find t to be not solvable. For t = 1, it's solvable, for t = 2 it's solvable and so on...
but when it's not?

Ok. Try setting



That's a determinant there. What do you get?

Whoops. That approach won't work. Take a look at this thread. Make sure you scroll all the way down to the end to get the real reason why that works.

I get a solution. Great.

It works, your approach works.

Wonderful. What is your value for t?

-(137/6)

That is correct.