Question

One equation of a pair of inconsistent linear equations is x-3y-5=0, then second equation can be
1. 2x-6y=10
2. -2x+6y=5
3. 3x+9y=5
4. x+3y=5

Answer 1

Given

One equation of a pair of inconsistent linear equations is x-3y-5=0

To find

second equation

Explanation

As they are inconsistent

real solutions does not exist

So,they must be coincident lines

The condition for the coincident lines is

$\boxed{\bf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}$

Here one of the lines is given

x-3y-5=0

$a_1=1\\ b_1=-3 \\ c_1=-5$

Consider the options

Option 1

2x-6y-10=0

$a_2=2\\b_2=-6\\c_2=-10$

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{1}{2}$

Here all the ratios are equal

Option 2

-2x+6y-5=0

$\dfrac{-1}{2}=\dfrac{-1}{2}\neq1$

Option 3

3x+9y-5=0

$\dfrac{1}{3}\neq\dfrac{-1}{3}\neq1$

Option 4

x+3y-5=0

$1\neq(-1)=1$

only in option 1 the condition is satisfied

So,that answer is option 1