For what value of k does the system of equations x+2y=3,5x+ky+7=0 have(i) a unique solution,(ii) no solution?

Also,show that there is no value of k for which the given system of equations has infinitely many solutions.

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Solution

The given equation be as:
x + 2y -3 = 0....(1)
5x + ky + 7 = 0....(2)

We have,

(i) For unique solution;

(ii)For No solution;
$a subscript 1 over a subscript 2 equals b subscript 1 over b subscript 2 not equal to c subscript 1 over c subscript 2 space space semicolon 1 fifth equals 2 over k not equal to fraction numerator negative 3 over denominator 7 end fraction space space space space semicolon w h i c h space g i v e s semicolon k equals 10 space$

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For what value of k does the system of equations $k x + 2 y = 5, 3 x - 4 y = 10$ have

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