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The number of values of k, for which the system of equations (k + 1)x + 8y = 4k kx + (k + 3)y = 3k − 1 has no solution, is

1. infinite
2. 1
3. 2
4. 3

Correct answer: 1

Solution

Det = (k+1)(k+3)-8k = (k-1)(k-3) = 0 gives k=1 or k=3. At k=1 both equations become x+4y=2 (infinitely many solutions). At k=3 they give x+2y=3 and x+2y=8/3, which are inconsistent (no solution). So exactly 1 value of k.

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