The pair of equations $2x+ky=1$ and $3x-5y=7$ has a unique solution for:

A unique solution needs a₁b₂ − a₂b₁ ≠ 0, i.e. 2(−5) − 3k ≠ 0, so −10 − 3k ≠ 0 and k ≠ −10/3. Every other value of k gives exactly one intersection point; at k = −10/3 the two lines become parallel.