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

The correct option is B

$5x+4y=0$

Explanation for the correct option

Given $x+2y-10=0...\left(i\right)$

$2x+y+5=0...\left(ii\right)$

Multiply $\left(i\right)$ by $2$

$\Rightarrow 2x+4y-20=0...\left(i\right)$

Subtract $\left(ii\right)$ from $\left(i\right)$ and solve.

$\Rightarrow 3y-25=0$

We get $y=\frac{25}{3},x=-\frac{20}{3}$

The line should pass through the point $\left(-\frac{20}{3},\frac{25}{3}\right)$

Checking the options which satisfy the value of intersection point,

The required equation is $5x+4y=0$

Hence the correct option is option B.