Question

Find the value of k, for which the system of equations 2x + 3y = 0 and
3x + ky = 0 has a unique solution.​

Answer 1

Answer:

2x+3y=0 and 3x+ky=0

a1=2 b1=3 a2=3 b2=k

a1/a2 =b1/b2

2/3 =3/k

3×3/2=k

9/2=k

Answer 2

for a equation to have a unique solution

a1/a2≠b1/b2

the given equations are---

(i)2x + 3y = 0

(ii)3x + ky = 0

then,

       2/3≠3/k

    =>2k≠9

    =>k≠9/2

   =>k≠4.5

hence both equation (i) and equation (ii) will have a unique solution for all values except 4.5

Hope this helps

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