Q.3. For what value of k, the pair of linear equations 2x + 3y = 7 and 5x + ky = 9 has a unique
solution ?
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Given : pair of linear equations 2x + 3y = 7 and 5x + ky = 9 has a unique
solution
To Find : Value of k
Solution:
Pair of lines
a₁x + b₁y = c₁ &
a₂x + b₂y = c₂
has unique solution iff
a₁/a₂ ≠ b₁/b₂
2x + 3y = 7
5x + ky = 9
unique solution iff
2/5 ≠ 3/k
=> k ≠ 15/2
value of k for unique solution :
k ≠ 15/2
k ∈ R - {15/2}
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