Question

If the lines $3x+2ky=2$ and $2x+5y+1=0$ are parallel, then find the value of $k$.

Answer 1

Suppose that we have to parallel lines $a_{1}x+b_{1}y+c_1=0\&a_{2}x+b_{2}y+c_2=0$ then,ratio of coefficient of x and y are equal i.e. $\frac{a_1}{a_2}=\frac{b_1}{b_2}$.

Now, according to given equations

$3x+2ky=2$

$2x+5y+1=0$

compairing coeffient of x& y and applying rule,

$\frac{3}{2}=\frac{2k}{5}$

$\Rightarrow 4k=15$

So value of $k=\frac{15}{4}$.