Question

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

(ii) Parallel lines

Answer 1

Writing another linear equation:

For parallel lines, we know that

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

Here

$a_1=2,b_1=3,c_1=-8$

So we can take

$a_2=2,b_2=3,c_2=5$

So the equation for a parallel line is

$2x+3y+5=0$

Hence, another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines is given.