Question

Equation of a line passing through the intersection of the lines $x+2y-10=0$ and $2x+y+5=0$ is

• A. $3x+3y=45$
• B. $15x+18y-50=0$
• C. $2x+3y=5$
• D. $18x+15y-50=0$

Answer 1

Answer: (B)

$15x+18y-50=0$

The point of intersection of $x+2y-10=0$ and $2x+y+5=0$ is $(\frac{-20}{3},\frac{25}{3})$

And substituting this in options

(A) $3x+3y=45$

$\Rightarrow 3\left(\frac{-20}{3}\right)+3\left(\frac{25}{3}\right)=45$

$\Rightarrow -20+25=45\Rightarrow 5\ne 45.$

(B) $15x+18y-50=0$

$\Rightarrow 15\left(\frac{-20}{3}\right)+18\left(\frac{25}{3}\right)-50=0$

$\Rightarrow -100+150-50=0\Rightarrow 0=0.$

(C) $2x+3y=5\Rightarrow 2\left(\frac{-20}{3}\right)=3\left(\frac{25}{3}\right)=5$

$\Rightarrow \frac{-40}{3}+25\ne 5.$

(D) $18x+15y-50=0$

$\Rightarrow 18\left(\frac{-20}{3}\right)+15\left(\frac{25}{3}\right)-50=0$

$\Rightarrow -120+125-50=0$

$\Rightarrow 45\ne 0$

Hence only option (B) is correct.