Question

Find the value of ‘k’ if the given equations are having unique solutions.

2x – ky + 7 = 0 and 3x + 6y – 9 = 0​

Answer 1

Step-by-step explanation:

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Answer 2

Given :-

2x - ky + 7 = 0 ................(1)

3x + 6y - 9 = 0 ................(2)

To find :-

the value of K if the equation have unique Solution.

here,

for eq. (1) a = 2 ; b = -k ; c = 7

for eq. (2) a = 3 ; b = 6 ; -9

we know that :-

$\sf \: for \: unique \: solution \: of \: the \: equation \: - \\ \\ \implies \sf \: \dfrac{a1}{a₂} ≠ \: \dfrac{b1}{b₂}$

i.e

$\implies \: \sf \: \dfrac{2}{3} \: ≠ \: \dfrac{ - k}{6} \\ \\ \implies \: \sf \: \dfrac{2}{ \cancel3} \: ≠ \: \dfrac{ - k}{² \: \cancel6} \\ \\ \implies \: \sf \: \: - k \: ≠ \: 4 \\ \\ \implies \: \sf \: \: k \: ≠ \: - 4$

therefore all the values of k except (-4) will have unique Solution .

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