Find the equation of the line through the intersection of the lines 3x+y-9=0 and 4x+3y-7=0 and which is perpendicular to the line 5x-4y+1=0.

Find the equation of the line through the intersection of the lines 3x

1.	Find the equation of the line through the intersection of the lines 3x+y-9=0 and 4x+3y-7=0 and which is perpendicular to the line 5x-4y+1=0.
Answer» `5x-4y+1=0 Rightarrow y=(5)/(4)x+(1)/(4)` Slope of this given line is `(5)/(4)` Now, the equatoin of any line through the intersection of the given line is of the form `(3x+y-9)+k(4x+3y-7)=0......(i)` `Rightarrow (3+4k)x+(1+3k)y-(9+7k)=0` `Rightarrow (1+3k)y=-(3+4k)x+(9+7k)` `Rightarrow y=-((3+4k))/((1+3k))x+((9+7k))/((1+3k))..............(ii)` Let m be the slope of the line perpendicular to the required line. `"Then,"mxx(5)/(4)-1 Rightarrow m=(-4)/(5)` `"Then,"mxx(5)/(4)-1 Rightarrow m=(-4)/(5)` `therefore "we must have"(-(3+4k))/((1+3k))=(-4)/(5)` `Rightarrow 15+20k=4+12k Rightarrow 8k=-11 Rightarrow k=(-11)/(8)` Substituting `k=(-11)/(8)(4+3y-7)=0` `(3x+y-9)-(11)/(8)(4+3y-7)=0` `Rightarrow (24x+8y-72)-44x-33y+77=0` `Rightarrow 20x+25y-5=0 Rightarrow 4x+5y-1=0`

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Find the equation of the line through the intersection of the lines 3x+y-9=0 and 4x+3y-7=0 and which is perpendicular to the line 5x-4y+1=0.

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