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2 answers:
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Suppose we choose 
and 
. Then
Now suppose we choose
such that
where we pick the solution for this system such that
. Then we find
Note that you can always find a solution to the system above that satisfies as long as 
. What this means is that you can always find the value of 
as a (constant) function of 
.
Now suppose we choose
where we pick the solution for this system such that
Note that you can always find a solution to the system above that satisfies
Answer: The statements in options 2 and 4 are true.
Explanation:
The LCM of two numbers is the smallest number that is multiple of both numbers.
The factor of 8 and 12 are,
Since 2 and 2 are common in both but 2 and 3 are not same, therefore the L.C.M. of 8 and 12 is,
Therefore the statement in option 1 is incorrect.
The factor of 6 and 9 are,
Since 3 is common in both but 2 and 3 are not same, therefore the L.C.M. of 6 and 9 is,
Therefore the statement in option 2 is correct.
The factor of 11 and 4 are,
Since all factor are different, therefore the L.C.M. of 11 and 4 is,
Therefore the statement in option 3 is incorrect.
The factor of 9 and 10 are,
Since all factor are different, therefore the L.C.M. of 9 and 10 is,
Therefore the statement in option 4 is correct.