Question

Question 4 (i)
Find the value(s) of p for the pair of equations 3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel.

Answer 1

Given pair of linear equations is
3x – y – 5 = 0
and 6x – 2y – p = 0
On comparing with ax + by + c = 0, we get
$a_1=3,b_1=-1,c_1=-5a_2=6,b_2=-2,c_2=-p$
Since, the lines represented by these equations are parallel, then
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
$\Rightarrow \frac{3}{6}=\frac{-1}{-2}\ne \frac{-5}{-p}$
Taking last two parts, we get $\frac{-1}{-2}\ne \frac{-5}{-p}$
$\Rightarrow \frac{1}{2}\ne \frac{5}{p}\Rightarrow p\ne 10$
Hence, the given pair of linear equations are parallel for all real values of p except 10 i.e., p $ϵ$ R – {10},where R is the set of real numbers.