**Question:**

Given the linear equation 2*x* + 3*y* − 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is :

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines

**Solution:**

(i) Given the linear equation are: $2 x+3 y-8=0$

We know that intersecting condition:

$\frac{a 1}{a 2} \neq \frac{b 1}{b 2}$

Where $a_{1}=2, b_{1}=3, c_{1}=-8$

Hence the equation of other line is $x+2 y-4=0$

(ii) We know that parallel line condition is: $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}$

Where $a_{1}=2, b_{1}=3, c_{1}=-8$

Hence the equation is $2 x+6 y-12=0$

(iii) We know that coincident line condition is: $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Where $a_{1}=2, b_{1}=3, c=-8$

Hence the equation is $4 x+6 y-16=0$