system of equations: no solution, unique solution, infinitely many solutions

Hey guys,

I have to solve the following problem:

Let the following systems of equations be given:

i)

2x 1 − 3x 2 + x 3 = 4

x 1 − 4x 2 − x 3 = 2

− 3x 1 + tx 2 − 2x 3 = − 3

ii)

x 2 − x 3 = 2

− x 1 + 2x 2 − 4x 3 = 3

x 1 − x 2 + 3x 3 = t + 1

For which values of t does the system have

a) a unique solution? Find this solution.

b) inﬁnitely many solutions? Find the solution set.

c) no solution?

So I started with the first one and get

x2 = -7/(8+t)

so I guess c) if t=8 the system has no solution.

For the others I just don't know how to proceed... Thanks for any help. :)

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Re: system of equations: no solution, unique solution, infinitely many solutions

Re: system of equations: no solution, unique solution, infinitely many solutions

Thank you ibdutt. This is very helpful but using this method in this special case I get:

for no solution: 5/(8+t) = 3/0

for infinitely many solutions: 5/(8+t) = 3/0 = 0/7

for unique solution: 5/(8+t) /= 3/0

....??

Re: system of equations: no solution, unique solution, infinitely many solutions

Quote:

Originally Posted by

**pesto** Thank you ibdutt. This is very helpful but using this method in this special case I get:

for no solution: 5/(8+t) = 3/0

which is the same as 0(5)= 2(8+ t). What does that tell you?

Quote:

for infinitely many solutions: 5/(8+t) = 3/0 = 0/7

Which is the same as 3(7)= 0. What does that tell you?

Quote:

for unique solution: 5/(8+t) /= 3/0

Which is the same as 3(8+t) is NOT equal to 0. What does that tell you?

Re: system of equations: no solution, unique solution, infinitely many solutions

well maybe that there is no solution for t = -8 and a unique solution for t /= -8 and that there are no infinitely many solutions..?

But if all t /= -8 have a unique solution I would think that there are infinitely many?!