Question

For what value of K the system of linear equations 2x +ky = 1 ; 3x - 5y = 7 has a unique solutios

• A. $K\ne -\frac{10}{3}$
• B. $K\ne \frac{10}{3}$
• C. $K\ne -35$
• D. $K-\frac{10}{3}$

Answer 1

The correct option is A $K\ne -\frac{10}{3}$

The equations will have unique solutions only if they are not parallel.
This means, their slopes should not be equal.
$=>-\frac{2}{k}\ne -\frac{3}{-5}$
$=>K\ne -\frac{10}{3}$