SOLUTION: the pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not have any solutions if k = ?

Question 924054: the pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not have any solutions if k = ?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
given:
the pair of linear equations

find: such that the pair of linear equations does not have any solutions
recall:
if solving a linear system, in fact there are only three possible cases:
No solution
One solution
Infinitely many solutions
When there is the equations are called "inconsistent" and the lines are
One or infinitely many solutions are called "consistent"-overlapping lines

so, your lines be parallel, and they will be parallel if they have

now, solve your line for

=> slope is

=> slope is
now, since , we have
-solve for
...both sides multiply by

then your system is:

_________________________________
see the graph:

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