Question

Find equation of the st. line passing through point of intersection of two St.lines L1 : 3x+5y+2=0 , L2 :x-y-4=0 and cuts from postivie part of x-axis 2 length unit

Answer 1

Point of intersection is:
3x+5y+2=0
x-y=4
3(4+y)+5y+2=0
12+9y+2=0
y=14/9
x=14+36/9=50/9
So, for 1 point we have (50/9,14/9)
For second, from the task we have (2,0)
So, from equation of the line by 2 points we have:
14x/9-(50-2)y/9-10/9=0
14x-48y=28
7x-24y=14