Question

The straight line passes through the point of intersection of the straight lines $x+2y-10=0$ and $2x+y+5=0$, is

• A. $5x-4y=0$
• B. $5x+4y=0$
• C. $4x-5y=0$
• D. $4x+5y=0$

Answer 1

Answer: (B)

$5x+4y=0$

The line passes through the point of intersection of the equations $x+2y-10=0$ and $2x+y+5=0$

Now,

$x+2y-10=\mathrm{0....}\left(i\right)2x+y+5=\mathrm{0....}\left(ii\right)\times 2=>4x+2y+10=\mathrm{0....}\left(iii\right)$

Subtracting (iii) and (i), we get,

$-3x-20=0=>x=\frac{-20}{3}\therefore y=\frac{25}{3}$

Now the line must pass through $(\frac{-20}{3},\frac{25}{3})$

Therefore, $5x+4y=0$ passes through $(\frac{-20}{3},\frac{25}{3})$