# State whether the following statement is true or false and justify : The straight line $5x + 4y = 0$ passes through the point of intersection of the straight lines $x + 2y – 10 = 0$ and $2x + y + 5 = 0$

Toolbox:
• If three lines are concurrent then $\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix} =0$ is the condition for concurrency.
It is given that $5x+4y=0$ passes through the intersection of the straight lines $x+2y-10$ and $2x+y+5$.
$\therefore \begin{vmatrix} 1 & 2 & -10 \\ 2 & 1 & 5 \\ 5 & 4 & 0 \end{vmatrix}$
$= 1(0-20)-2(0-25)-10(8-5)$
$= -20+50-30$
$= 0$
Hence it is a true statement.