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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The number of values of $k$ for which the system of equations
$(k+1)x + 8y = 4k$ and $kx + (k+3)y = 3k-1$ has infinitely many solutions, is
Solution
$ (k+1)x + 8y = 4k $$ kx + (k+3)y = 3k - 1 $
Since the system has infinitely many solutions,
$ \dfrac{k+1}{k} = \dfrac{8}{k+3} = \dfrac{4k}{3k-1} $
Taking 1st and 3rd ratio:
$ (k+1)(3k-1) = 4k^2 $
$ 3k^2 + 2k - 1 = 4k^2 $
$ k^2 - 2k + 1 = 0 $
$ (k-1)^2 = 0 $
$ \therefore k = 1 $
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