Question

The straight line $5x+4y=0$ passes through the point of intersection of the straight lines $x+2y-10=0$ and $2x+y+5=0$. State whether the statement is true or false. Justify

Answer 1

Given : $x+2y-10=0$ ⋯(1)

and $2x+y+5=0$

$\Rightarrow y=-5-2x$ ⋯(2)

From equations (1) and (2), we get

$x+2(-5-2x)-10=0$

$\Rightarrow -3x-20=0$

$\Rightarrow x=-\frac{20}{3}$

$\Rightarrow y=-5+\frac{40}{3}=\frac{25}{3}$

So, the point of intersection is $(-\frac{20}{3},\frac{25}{3})$

Checking whether this point lies on

$5x+4y=0$ or not.

$5(-\frac{20}{3})+4\left(\frac{25}{3}\right)=\frac{-100+100}{3}=0$

So, the point of intersection $(-\frac{20}{3},\frac{25}{3})$ lies on the line $5x+4y=0$

Hence the given statement is true.