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प्रश्न
In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
kx + 2y - 5 = 0
3x + y - 1 = 0
उत्तर
The given system of equation is
kx + 2y - 5 = 0
3x + y - 1 = 0
The system of equation is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0``
Where `a_1 = k, b_1 = 2, c_1 = -5`
And `a_2 = 3, b_2 = 1, c_2 = -1`
For a unique solution, we must have
`a_1/a_2 != b_1/b_2`
`:. k/3 != 2/1`
`=>? k != 6`
So, the given system of equations will have a unique solution for all real values of k other than 6.
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