Question

write the value of K for which the system of equation 3x + Ky = 0 and 2x - y = 0 has a unique solution

Answer 1

The system of equations is:

3x + Ky = 0
2x - y = 0

For a unique solution,
$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

here, a1 = 3, b1 = k, a2 = 2, b2 = -1

$\frac{a_1}{a_2} \neq \frac{b_1}{b_2} \\ \\ \frac{3}{2} \neq \frac{k}{ - 1} \\ \\ \frac{3}{2} \times ( - 1) \neq k \\ \\ k \neq \frac{ - 3}{2}$

Thus k ≠ -3/2. k can be any value except -3/2.

So possible values of k are 2, 3, 5, -100 etc.
You can take anything. Just do not take k as -3/2.

Answer 2

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