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  • The value of c for which the pair of linear equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value

The value of c for which the pair of linear equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(A) 3
(B) – 3
(C) –12
(D) no value

Answers (1)

Answer: D
Solution:
Equations are
cx – y – 2 = 0, 6x – 2y – 3 = 0
In equation
cx – y – 2 = 0
a1 = c, b1 = –1, c1 = –2
In equation
6x – 2y – 3 = 0
a2 = 6, b2 = –2, c2 = –3
Since equations have infinitely many solutions
Hence \frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}= \frac{c_{1}}{c_{2}}
\frac{c}{6}= \frac{-1}{-2}\neq \frac{-2}{-3}
Here we find that \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}} i.e., equations are inconsistent

So, we can not assign any value to c.

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infoexpert27

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