For what value of $k$ does the pair of equations $2x+ky=1$ and $3x-5y=7$ have a unique solution?
$k=-\dfrac{10}{3}$
$k
eq-\dfrac{10}{3}$
$k=0$
$k=1$
Step-by-Step Solution
Key Concept: Apply the condition $\dfrac{a_1}{a_2}<br>eq\dfrac{b_1}{b_2}$.
Unique solution requires $\dfrac{2}{3}
eq\dfrac{k}{-5}$. [0.5 Mark]
$\dfrac{k}{-5}=\dfrac23 \Rightarrow k=-\dfrac{10}{3}$ is the excluded value, so the condition is $k
eq-\dfrac{10}{3}$. [0.5 Mark]
Correct Answer: $k\neq-\dfrac{10}{3}$