For what values of and , the simultaneous equations
i) no solution
ii) a unique solution
iii) an infinite number of solution
(You will need to check this result very carefully because my algebra and arithmetic is well known to be terrible).
Examine it carefully. The interpretation of the following cases is left for you:
Case 1: .
Case 2: .
Case 3: .
You seem to be losing your connection with what it is you are trying to do.
Try this version:
Use the first equation to eliminate 'x' in the other two.
Now use the first to eliminate y from the second.
Now, reread the problem statement and see if you can make any inferences from this information.
If [tex]\lambda- 5[/itex] is NOT 0, we can divide both sides by that to get a specific value for z and then it would be easy to solve for x and y. As long as is not 0, we have a unique solution.
If , in other words if we cannot divide to find z but if it also happens that that equations just says "0z= 0" which is true for all z. If [tex]\lamba= 5[/itex] and , there are an infinite number of solutions.
If and is NOT 14, then 0z would have to be equal to a non-zero number and that is impossible. If and is not 14, there is no solution.