Question

Find the value of $p$ for which the system
$2x+py=1$
$3x-5y=7$
will have a unique solution

• A. $p=-\frac{10}{3}$
• B. $p=7$
• C. $p\ne -\frac{10}{3}$
• D. $p\ge -\frac{10}{3}$

Answer 1

The correct option is C $p\ne -\frac{10}{3}$

To have an unique solution, the lines should not be parallel to each other. This means their slopes are not equal
$=>-\frac{2}{p}\ne -\frac{3}{5}$
$=>p\ne -\frac{10}{3}$