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The value of k for which the system of equestions kx-y=2 and 6x-2y=3 has a uniqe solution is..
Asked by ruchipandey20071978 | 11 May, 2023, 06:55: AM
answered-by-expert Expert Answer
Given equations are as follows:
k x minus y equals 2 space a n d space 6 x minus 2 y equals 3 rightwards double arrow k x minus y minus 2 equals 0 space space a n d space space 6 x minus 2 y minus 3 equals 0
 
This is of the form
a subscript 1 x plus b subscript 1 y plus c subscript 1 equals 0 space space a n d space space a subscript 2 x plus b subscript 2 y plus c subscript 2 equals 0 w h e r e a subscript 1 equals k comma space b subscript 1 equals negative 1 comma space c subscript 1 equals negative 2 a subscript 2 equals 6 comma space b subscript 2 equals negative 2 comma space c subscript 2 equals negative 3
For a unique solution, we must have
a subscript 1 over a subscript 2 not equal to b subscript 1 over b subscript 2 rightwards double arrow k over 6 not equal to fraction numerator negative 1 over denominator negative 2 end fraction rightwards double arrow k over 6 not equal to 1 half rightwards double arrow k not equal to 6 over 2 not equal to 3
Hence, the given system of equations will have a unique solution when k not equal to 3.
Answered by Rashmi Khot | 11 May, 2023, 10:21: AM

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