Question

if 2x-ky=5 is parallel to 3x+4y-7=0, find the value of k

Answer 1

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since the graph of two equations are parallel, hence they have no solution.
we know the condition for no solution
i.e.,

a1/a2 = b1/b2 ≠ c1/c2

here,
a1 = 2
a2 = 3
b1 = - k
b2 = 4
c1 = -5
c2 = -7

so,

2/3 = 3/-k ≠ 5/7

2/3 = 3/-k

on cross multiplication,

-2k = 9

k = 9/-2