Question

We have a linear equation $2x+3y-8=0$. Write another linear equation in two variables x and y such that the geometrical representation of the pair so formed is intersecting lines.

Answer 1

Equation of first line is $2x+3y-8=0$

Let equation of second line be $ax+by+c=0$

For intersecting lines:$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Here $a_1=2,b_1=3,a_2=a,b_2=b$

Hence $\frac{2}{a}\ne \frac{3}{b}$ .......$\left(1\right)$

So, we assume a value of $a$ and $b$ such that equation $\left(1\right)$ is satisfied.

Let equation of second line be $3x+2y+4=0$

Here $a=3,b=2,c=4$ and equation is satisfied $\frac{2}{3}\ne \frac{3}{2}$