Thread: For which values of k are there no solutions, 1 solution, inifinite solutions.

1. For which values of k are there no solutions, 1 solution, inifinite solutions.

x-y = 1
3x - 3y = k

1 -1 ¦ 1
3 -3 ¦ k

1 -1 ¦ 1
0 0 ¦ k-3

so when k doesnt equal 3 there is no solutions

k = 3 infinite solutions

but i cant do the one solution, is there one? or have done it wrong?

Thanks 2. It looks like you've already answered your question. The problem is, the matrix you're dealing with is singular. That implies automatically, I think, that the existence of a unique solution is impossible. In other words, you've found all the possibilities. Just say there are no values of k for which the system has exactly one solution.

3. The two lines are parallel. What does that tell you?

4. Originally Posted by Plato The two lines are parallel. What does that tell you?
They don't cross, so there isn't one solution, cheers 5. It's probably more accurate to say that the lines, represented by the system of equations you have there, are either the same line, or non-intersecting, corresponding to infinite solutions and zero solutions, respectively. Does that make sense?

6. Originally Posted by Ackbeet It's probably more accurate to say that the lines, represented by the system of equations you have there, are either the same line, or non-intersecting, corresponding to infinite solutions and zero solutions, respectively. Does that make sense?
Yep it does, thanks for your time.

7. Great. You're very welcome. Have a good one!

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