If the system of linear equations 2x+3y=7 and kx+9y=15 has a unique solution, then value of is:

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k=6

k ≠ 6

k=-6

k ≠ − 6

answer is B.

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Detailed Solution

Given,
2x+3y=7 and kx+9y=15
Two lines

a x_{1} + {by}_{1} + c_{1} = 0

and

a x_{2} + {by}_{2} + c_{2} = 0

have a unique solution only if

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

.
Since, equations have a unique solution so,

a 1 a 2 ≠ b 1 b 2

⇒ 2 k ≠ 39 ⇒ k ≠ 6

Therefore, if the system of linear equations 2x+3y=7 and kx+9y=15 has a unique solution, then value of

is not equal to 6.
Hence, option 2 is correct.

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