Question

13. Find the value of k for which the following system of equations represent parallel lines

( k + 1 )x + 8y = 2 ;

2x + ( k +1 )y = 1

Standard:- 10

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Answer 1

Given Equation is (k + 1)x + 8y = 2 

= > (k + 1)x + 8y - 2 = 0 ------- (1)

Given Equation is 2x + (k + 1)y = 1 

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

a1 = (k + 1), b1 = 8, c1 = -2

a2 = 2, b2 = (k + 1), c2 = -1

Given that the Equations represent parallel lines:

= > (a1/a2) = (b1/b2) 

= > (k + 1)/2 = (8)/k + 1

= > (k + 1)^2 = 16

= > k + 1 = 4

= > k = 3.

Therefore the value of k = 3.



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