Question

For which of the following values of k will the system of equations $2x-5y=8,4x+ky=17$ have $\underset{–}{no}$ solution?

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

Answer 1

The correct option is A $-10$

A system of two linear equations has no solution when the lines are parallel.

$2x–5y=8$

$\Rightarrow$ $5y=2x-18$

$y=\frac{2}{5}x–\frac{18}{5}$

$\therefore m_1=\frac{2}{5}$

$4x+ky=17$

$\Rightarrow$ $ky=17-4x$

$y=-\frac{4}{k}x+\frac{17}{k}$

$\therefore m_2=-\frac{4}{k}$

Parallel lines have the same slope-

$\therefore m_1=m_2$

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

$\Rightarrow 2k=-20$

$\Rightarrow k=-10$