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Question

The number of values of k for which the system of equations (k+1)x + 8y = 4k, kx + (k+3)y = 3k1 has infinitely many solutions, is

A
\N
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B
1
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C
2
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D
Infinite
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Solution

The correct option is B 1
For infinitely many solutions, the two equations must be identical
k+1k = 8k+3 = 4k3k1 (k+1)(k+3) = 8k and 8(3k-1) = 4k(k+3)
k24k+3 = 0 and k23k+2 = 0 .
By cross multiplication, k28+9 = k32 = 13+4
k2 = 1 and k=1 ; k=1.

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