# Answer to Question #20563 in Analytic Geometry for samy

Question #20563

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

Expert's answer

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

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

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