The equation of the line passing through the point of intersection of the lines 2 x+3 y+6=0,3 x-y-13=0 and parallel to the line 3 x-4 y+5=0 is

Step-by-step solution

Let L₁ 2 x+3 y+6=0 L₂ 3 x-y-13=0 Equation of line passing through the point of intersection. array r L₁+ L₂=0 (2 x+3 y+6)+ (3 x-y-13)=0 (2+3 ) x+(3- ) y+6-13 =0 array Which is parallel to the line 3 x-4 y+5=0 On comparing the coefficient, we get aligned 2+3 3 = 3- -4 & = 6-13 5 -8-12 & =9-3 aligned =- 17 9 putting this value in required equation, we get array rlrl (2- 51 9 ) x+ (3+ 17 9 ) y+6+ 221 9 & =0 & & -33 x+44 y+275 & =0 & & 3 x-4 y-25 & =0 . array