For what value of k does the following pair of linear equations have no solution?

$10 x + 5 y - (k - 5) = 0 a n d 20 x + 10 y - k = 0.$

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Solution

$c o n d i t i o n space f o r space n o space s o l u t i o n space i s space fraction numerator a 1 over denominator a 2 end fraction equals fraction numerator b 1 over denominator b 2 end fraction not equal to fraction numerator c 1 over denominator c 2 end fraction p u t t i n g space v a l u e s space 10 over 20 equals 5 over 10 not equal to fraction numerator negative open parentheses k minus 5 close parentheses over denominator negative k end fraction 1 half not equal to fraction numerator k minus 5 over denominator k end fraction k not equal to 2 k minus 10 k not equal to 10 space$

for all real values of K except 10 will give no solution

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10 x + 5 y - (k - 5) = 0

20 x + 10 y - k = 0

10 x + 5 y - (k - 5) = 0 20 x + 10 y - k = 0

For what value of k will the following pair of linear equation have no solution?

$2 x + 3 y = 9, 6 x + (k - 2) y = (3 k - 2) .$

(3 k + 1) x + 3 y - 2 = 0

(k^{2} + 1) x + (k - 2) y - 5 = 0

5 x + 2 y = k; 10 x + 4 y = 3

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