Find k if k x – y – 2 = 0 and 6 x – 2y – 3 = 0 have infinite solutions
(a) k = 3
(b) k = -3
(c) k = 0
(d) none of these
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Answer:
(d) none of these
Step-by-step explanation:
If these equations had infinite solutions, they would form lines in which the y-intercept and slope are the same.
Put each equation in to slope-intercept (y=mx+b) form:
kx-y-2=0
-y=-kx+2
y=kx-2
6x-2y-3=0
-2y=-6x+3
y=3x-3/2
Clearly, these equations form lines with two different y-intercepts: (0, -2) and (0, -3/2). Therefore, there is no k value that can make the equations have infinite solutions.
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