For what value of k, the pair of linear equations x+2y=3,5x + ky +7 =0 represents
(1) Intersecting lines
(1) Parallel lines Is there any value of k for which the given equations represent coincident lines?
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Step-by-step explanation:
Given, pair of linear equations are
x+2y=3, 5x + ky +7 =0
(1) Intersecting lines
=> a1/a2 ≠ b1/b2
=> 1/5 ≠ 2/k
=> k ≠ 10
(2) Parallel lines
=> a1/a2 = b1/b2 ≠ c1/c2
=> 1/5 = 2/k ≠ -3/7
=> k = 10 ≠ -14/3
(3) Coincident lines
=> a1/a2 = b1/b2 = c1/c2
=> 1/5 = 2/k = -3/7
=> k = 10 or -14/3
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