1
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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=3kâˆ’1 has no solution is

A
1
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B
3
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C
2
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D
infinite
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Solution

## The correct option is A 1Let △=∣∣∣k+18kk+3∣∣∣=k2+4k+3=(k−1)(k−3)For the system of equation to have no solution △=0⇒k=3,1For k=1, the system of equation becomes 2x+8y=4 and x+4y=2⇒x+4y=2,x+4y=2This system has infinite number of solution For k=3, the system of equation becomes 4x+8y=12 and 3x+6y=8⇒x+2y=3,x+2y=83Thus, in this case the system of equation has no solution.The number of values of k for which the given system of equations has no solution is 1.

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