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Pair of Linear Equations in Two Variables
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27/05/2021 12:09 pm
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For which value of k will the following pair of linear equations have no solution?
3x + y = 1
(2k – 1) x + (k – 1) y = 2k + 1
1 Answer
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27/05/2021 12:10 pm
Given, 3x + y -1 = 0
(2k -1)x + (k-1)y – 2k -1 = 0
a1/a2 = 3/(2k -1), b1/b2 = 1/(k-1), c1/c2 = -1/(-2k -1) = 1/(2k +1)
For no solutions
a1/a2 = b1/b2 ≠ c1/c2
3/(2k-1) = 1/(k -1) ≠ 1/(2k +1)
3/(2k –1) = 1/(k -1)
3k -3 = 2k -1
k = 2
Therefore, for k = 2 the given pair of linear equations will have no solution.