Question

$2x-5y=8$
$4x+ky=17$
For which of the following values of $k$ will the system of equations above have no solution?

• A. $-10$
• B. $-5$
• C. $0$
• D. $5$
• E. $10$

Answer 1

The correct option is A $-10$

Given equations are $2x-5y=8$ and $4x+ky=17$.

The system of equation will not have solution, if both are parallel.

Slope of $2x-5y=8$ is $\frac{-2}{-5}=\frac{2}{5}$.

and slope of $4x+ky=17$ is $-\frac{4}{k}$.

$\Rightarrow \frac{2}{5}=-\frac{4}{k}$

$\Rightarrow k=-10$