Question

find the eqn. of the line drawn through the point of intersection of the lines 4x-3y+7=0 and 2x+3y+5=0 and passing through the point (-4,5).

Answer 1

first of all solve this two given equation
4x-3y+7=0-------(1)
2x+3y+5 =0-------(2)
(1)+(2)
6x+12=0
x=-2
put x =-2 in equation (1)
y=-1/3
hence given equation intersecting point (-2,-1/3)
now
we have two point (-4,5) and (-2,-1/3)

slope of equation of line =(-1/3-5)/(-2+4)
=-8/3
now equation of line
(y-5)=-8/3 (x+4)
=>3 (y-5)+8 (x+4)=0
=> 8x+3y+17=0