Question

Given the linear equation $5x-2y=4$5x−2y=4 , Write another linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines

Answer 1

Step 1:

General form of linear equation

We have the general form for a pair of linear equations in two variables $x$ and $y$ is ,

$a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$where, $a_1,a_2,b_1,b_2,c_1,c_2$are the real numbers

Step 2:

Condition for parallel lines

A pair of linear equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$is parallel if

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

Step 3:

Finding second linear equation

Given equation is,

$5x-2y-4=0$

$ie,a_1=5,b_1=-2and{c}_1=-4.$

Therefore any line parallel with the given equation may be taken as

$10x-4y-6=0or5x-2y-3=0$