find the equation of the line which pass through the point of intersection of the lines 4x-3y-1=0 & 2x-5y+3=0 and is equally inclined to the axes

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Please find below the solution to the asked query:

Let point of intersection be x1,y14x-3y-1=0 ;equationi2x-5y+3=0 ;equationiiequationi-2×equationii, we get,4x-3y-1-4x-10y+6=04x-3y-1-4x+10y-6=07y=7y=1Pu this value of y in equationi, we get,4x-3-1=0x=1x1,y1=1,1Now since required line is equally inclined to axes.Angle made by line with positive direction of x-axis may be 45° or 135°.Case i m=tan 45°m=1Equation of line is given by,y-y1=mx-x1y-1=1x-1x-y=0Case ii m=tan 135°m=-1Equation of line is given by,y-y1=mx-x1y-1=-1x-1y-1=-x+1x+y=2Hence required equations of line are x-y=0 and x+y=2.

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