Question

For what value of m do the equations 3x + my = 10 and 9x + 12y = 30 have a unique solution.

Answer 1

Hey there !!


We are given that -

3x + my - 10 =0

And
9x + 12 y - 30 =0

Where

a₁ = 3 , b₁ = m , c₁ = -10

And

a₂ = 9 , b₂ = 12 , c₂ = - 30

We know the condition

If a₁/b₂ ≠ b₁/₂

So putting all the required values over here

3/9 ≠ m/12

=> 1/3 ≠ m/12

=> 3m ≠ 12

=> m ≠ 4

Hence if the value of m apart from 4 then it will have unique soln

Hope this would help you !!