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(39617) (Show Source): You can put this solution on YOUR website!
;
The second equation is .
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 will work. As long as , the two lines will intersect in exactly one point.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The lines can't be parallel, or the same line repeated
(1)
Add to both sides
(1)
Add to both sides
(1)
Write it the other way
(1)
----------------------
(2)
Switch the terms on the right
(2)
Divide both sides by
(2)
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These lines will be the same line
repeated if
For any other value of ,
the lines will meet at one point
---------------------------
or
is the answer
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