Need help with cramer's rule, applied linear algebra

Question

anonymous · Answer

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anonymous · Answer

so i know $$x= \frac{ (4k^2-60k) }{ -18k }$$
and $$y= \frac{ (2k^2-30k) }{ (2k-3) }$$
after doing the cramers rule, but I dont understand how to find the unique solution?

anonymous · Answer

do I just plug those equations into the original equations and solve for "k" to get the value of k when the system has a unique solution?

anonymous · Answer

woops sorry didnt realize that they do not want an actual value for "k" they just want an expression.

amistre64 · Answer

when are we assured that a unique solution exists in a system of 2 lines?

amistre64 · Answer

if 2 lines have the same slope, they are either the same line; or they never meet.  either way, there is no one solution to them.

lines must have different slopes in order to meet at one point.