find the equation of line passing through the point of intersection of 2x+y+6=0 and 3x+5y-15=0 and parallel to the line 5x+6y+3=0
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Step-by-step explanation:
2x+y= -6-------1
3x+5y=15-------2
equation1 × 5-equation2
10x+5y=-30
3x+5y= -15
__________
7x = -15
X= -15/7
from 1
2(-15/7)+y=-6
Y= -6+30/7
=(-42+30)/7
= -12/7
point of intersection (-15/7, -12/7)
slope of 5x+6y+3=0 is m= _5/6
equation of required line =( y-y1) = m(x-x1)
y-(-12/7) =-5/6 (x-(-15/7))
(7y+12)/7= -5/6(7x+15)/7
6(7y+12)=-5(7x+15)
42y+72= -35x - 75
35x+42y+147= 0
equation of the required line = 35x+42y+147= 0
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