if A and B are two arbitrary constants then the straight line (a-2b)x+(a+3b)y+3a+4b=0 will pass through - Maths - Straight Lines

Question

if A and B are two arbitrary constants then the straight line
(a-2b)x+(a+3b)y+3a+4b=0 will pass through

Ankita Agarwal · Accepted Answer

Dear Student ,
Given Equation : a-2bx+a+3by+3a+4b=0can be written as , ax-2bx+ay+3by+3a+4b=0ax+y+3+b-2x+3y+4=0x+y+3+ba-2x+3y+4=0Now , we have a points in the form of L1+λL2=0     we find this form of line , to find  when two lines are passes through a single intersection point Now lines passes through at their intersection points , which are to be found as Now , L1: x+y+3=0
iL2:-2x+3y+4=0
iiNow , Multiply by 2 in equation i and add it to equation ii2x+2y+6-2x+3y+4=05y+10=05y=-10y=-2Putting value of y in equation i we get , x=-1 Hence point of intersection is -1 , -2
Regards