Question

Find the value of p if the lines represented by these equations are parallel.

$3x+y+5=0and6x+2y+p=0$

Answer 1

Given equation,

$3x+y+5=0,6x+2y+p=0$

If the equations $a_{1}x+b_{1}y+c_1=0a_{2}x+b_{2}y+c_2=0$ represent parallel lines, then

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

So, from given equations,

$\frac{a_1}{a_2}=\frac{3}{6},$

$\frac{b_1}{b_2}=\frac{1}{2},$

$\frac{c_1}{c_2}=\frac{5}{p},$

$\because \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$,

So, $\frac{5}{p}\ne \frac{1}{2}$

$p\ne 10$

$\because p\in R-\left\{10\right\}$, to represent parallel lines.