Question

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

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

Answer 1

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

Given:
$L_1:2x+y-1=0,L_2:3x+2y-5=0$
The family of line through the intersection of $L_1$ and $L_2$ is
$L_1+\lambda L_2=0$
So,
$(2x+y-1)+\lambda (3x+2y-5)=0\cdots \left(1\right)$
Since, it passes through $(0,0)$, we get
$-1-5\lambda =0\Rightarrow \lambda =-\frac{1}{5}$

Putting the value of $\lambda$ in the equation $\left(1\right)$, we get
$2x+y-1-\frac{1}{5}(3x+2y-5)=0$
$\Rightarrow \frac{7}{5}x+\frac{3}{5}y=0$
$\therefore 7x+3y=0$