Question

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

A pair of linear equations have unique solution or intersecting at a point if

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Step 3:

Finding second linear equation

Given equation is,

$5x-2y-4=0$

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

So we can take $a_2=-2and{b}_2=5$ .

$c_2$can take any value

Hence, the second equation will be,$-2x+5y-3=0$.