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Question

Find the value of k so that the following system of equation has no solution

3x+y=1 (2k-1)x+(k-1)y=o

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Solution

3x+y-1=0
(2k-1)x+(k-1)y =0

here a1=3, b1=1 c1=-1
a2=(2k-1), b2=(k-1), c2=0

the following equation will have no solution
if a1/a2 = b1/b2 and both not equal to c1/c2

so, 3/(2k-1) = 1/(k-1)
or 3k-3 = 2k-1
or k = 2 Ans.

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