Question

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 1

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.