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proove that the lines 3x-4y+5=0 ,7x-8y+5=0 and 4x+5y=45 are concurrent also find the point of concurrency

$Given 3 x - 4 y + 5 = 0 - - - (i) 7 x - 8 y + 5 = 0 - - - (i i) 4 x + 5 y - 45 = 0 - - (i i i) If the lines are concurrent then | \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} | = 0 \Rightarrow | \begin{matrix} 3 & - 4 & 5 \\ 7 & - 8 & 5 \\ 4 & 5 & - 45 \end{matrix} | \Rightarrow 3 (36 0 - 25) + 4 (- 315 - 20) + 5 (35 + 32) \Rightarrow 3 (335) + 4 (- 335) + 5 (67) \Rightarrow 1005 - 1340 + 3354 \Rightarrow 0 So the given lines are concurrent To find point of concurrency solve any two equations and result should satisfy the third condition By solving (i) and (ii) we get x=5 and y=5 So the point of concurrency is (5,5)$

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