Question

If the lines given by 3x+2ky=8 and 2x+5y-4=0 are parallel then the value of k is

Answer 1

Given:

3x+2ky=8 and 2x+5y-4=0 are parallel

$\frac{\mathrm{a}_{1}}{\mathrm{a}_{2}}=\frac{\mathrm{b}_{1}}{\mathrm{~b}_{2}} \neq \frac{\mathrm{c}_{1}}{\mathrm{c}_{2}}$

3x+2ky=8 and 2x+5y-4=0

a1=3, b1=2k, c1=8 and a2=2, b2=5, c2=-4

$\therefore \frac{\mathrm{a}_{1}}{\mathrm{a}_{2}}=\frac{3}{2}, \quad \frac{\mathrm{b}_{1}}{\mathrm{~b}_{2}}=\frac{2 \mathrm{k}}{5} \text { and } \frac{\mathrm{c}_{1}}{\mathrm{c}_{2}}=\frac{8}{-4}=-2$

3/2=2k/5

k=3×5/2×2

k=15/4

Hence the value of k is 15/4