SOLUTION: determine the value of k so that the lines kx-y=-1/3 and 3y=1-6x will intersect at one point

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Question 893360: determine the value of k so that the lines kx-y=-1/3 and 3y=1-6x will intersect at one point
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
-y=-kx-1%2F3
highlight_green%28y=kx%2B1%2F3%29;

The second equation is highlight_green%28y=-2x%2B1%2F3%29.

If slopes were equal, k=-2, and these two lines would be the same identical line. To make them each DIFFERENT lines, then any k such that k%3C%3E-2 will work. As long as k%3C%3E-2, the two lines will intersect in exactly one point.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The lines can't be parallel, or the same line repeated
(1) +k%2Ax+-+y+=+-1%2F3+
Add +y+ to both sides
(1) +k%2Ax+=+y+-+1%2F3+
Add +1%2F3+ to both sides
(1) +k%2Ax+%2B+1%2F3++=+y+
Write it the other way
(1) +y+=+k%2Ax+%2B+1%2F3+
----------------------
(2) +3y+=+1+-+6x+
Switch the terms on the right
(2) +3y+=+-6x+%2B+1+
Divide both sides by +3+
(2) +y+=+-2x+%2B+1%2F3+
---------------------
These lines will be the same line
repeated if +k+=+-2+
For any other value of +k+,
the lines will meet at one point
---------------------------
+k+%3C+-2+ or +k+%3E+-2+
is the answer