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 of coincident lines.

• A. $4x+y-6=0$
• B. $4x+6y-16=0$
• C. $x+y-8=0$
• D. $x+y-16=0$

Answer 1

The correct option is B $4x+6y-16=0$

Equation of first line-

$2x+3y-8=0$

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

For coincident lines-

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

Here, $k$ is a numerical constant.

$\therefore$ To satisfy the above equation, if $k=2$, the equation of second line can be-

$4x+6y-16=0$