Question

The equation of the straight line through the intersection of line $2x+y=1$ and $3x+2y=5$ and passing through the origin, is:

• A. $7x+3y=0$
• B. $7x-y=0$
• C. $3x+2y=0$
• D. $x+y=0$

Answer 1

The correct option is A $7x+3y=0$

Family of straight lines passing through $2x+y-1=0$ and $3x+2y-5=0$ is:

$2x+y-1+\lambda (3x+2y-5)=0=>(2+3\lambda )x+(1+2\lambda )y-1-5\lambda =\mathrm{0....}\left(i\right)$

Given the line must pass through origin,

$\therefore (x,y)=(0,0)$ must satisfy equation (i)

$=>-1-5\lambda =0=>\lambda =\frac{-1}{5}$

After putting $\lambda =\frac{-1}{5}$, equation (i) becomes

$7x+3y=0$