Find the equation of the line through the intersection of lines `x+ 2y 3 = 0`and `4x y+ 7 =0` and which is parallel to `5x+ 4y 20 = 0`

Find the equation of the line through the intersection of lines `x+ 2y

1.	Find the equation of the line through the intersection of lines `x+ 2y 3 = 0`and `4x y+ 7 =0` and which is parallel to `5x+ 4y 20 = 0`
Answer» `5x+4y-20=0 Rightarrow y=(-5)/(4)x+5` `therefore "slope of the given lne"=(-5)/(4)` and slope of the required line =`(-5)/(4)` Now, the equation of any line through the intersection of hte given line of the form `(x+2y-3)+k(4x-y+7)=0` `Rightarrow (1+4k)x+(2-k)y+(7k-3)=0` `Rightarrow (2-k)y=-(1+4k)x+(3-7k)` `Rightarrow y=(-(1+4k))/((2-k))x+((3-7k))/((2-k))` `Rightarrow y=((1+4k))/((k-2))x+((3-7k))/((2-k))` Slope of this line =`((1+4k))/((k-2))` `therefore ((1+4k))/((k-2))=(-5)/(4)Rightarrow 4+16k=-5k+10` `Rightarrow 21k=6Rightarrow =(6)/(21)=(2)/(7)` Substituting `k=(2)/(7)` in (i), we get `(x+2y-3)+(2)/(7)(4x-y+7)=0` `Rightarrow (7x+14y-21)+(8x-2y+14)=0` `Rightarrow 15x+12y-7=0,` which is the required equation.

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Find the equation of the line through the intersection of lines `x+ 2y 3 = 0`and `4x y+ 7 =0` and which is parallel to `5x+ 4y 20 = 0`

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