Question

find k so that the equation has unique solution
2x+3y=7 & 2kx(k+m)y=2​

Answer 1

Given : 2x+3y=7  &  2kx + (k+2)y =2​

To find : k so that pair of linear equation has unique solution

Solution:

A pair of linear Equations

a₁x + b₁y  = c₁  &

a₂x + b₂y = c₂

has unique Solution  if

a₁/a₂  ≠ b₁/ b₂

2x+3y=7

2kx + (k+2)y =2​

=> 2/2k  ≠   3/(k + 2)

=> k + 2 ≠   3k

=> 2k ≠ 2

=> k ≠ 1

k ∈ R - {1}

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