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  • For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines (A)1by2 (B) –1by2 (C) 2 (D) –2

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?
(A) \frac{1}{2}
(B) –-\frac{1}{2}
(C) 2
(D) –2

Answers (1)

Answer: C
Solution:
Equations are
3x – y + 8 = 0
6x – ky + 16 = 0
In equation
3x – y + 8 = 0
a1 = 3, b1 = –1, c1 = 8
In equation
6x – ky + 16 =0
a2 = 6, b2 = –k, c2 = 16
\frac{a_{1}}{a_{2}}= \frac{3}{6}= \frac{1}{2}
\frac{b_{1}}{b_{2}}= \frac{-1}{-k}= \frac{1}{k}
\frac{c_{1}}{c_{2}}= \frac{8}{16}= \frac{1}{2}
Since lines are coincident
Hence \frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}= \frac{c_{1}}{c_{2}}
\frac{1}{2}= \frac{1}{k}= \frac{1}{2}….(i)
1/k = 1/2     ( from equation (1))
k = 2 Hence the value of k is 2.

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