Find the equation of the line through the intersection of 5x-3y-1=0 and 2x+3y-23=0 and

a)perpendicular to line whose equation is 5x-3y-1=0

b) parallel to the line 4x+5y-7=0

Point of intersection of  5x-3y-1=0 and 2x+3y-23=0 is (24/7 , 113/21 )

(a) : Perpendicular to 5x - 3y =1 will be -3x -5y = D
  $$\begin{gathered} -3\left(\frac{24}{7}\right) -5\left(\frac{113}{21}\right) =\mathrm{D} \\ \Rightarrow \mathrm{D} = -\frac{781}{21} \\ \mathrm{Thus}, \mathrm{reqd} \mathrm{line} \mathrm{is} : 3\mathrm{x} + 5\mathrm{y} = \frac{781}{21} \end{gathered}$$
(b) Line parallel to  4x + 5y =7 will be 4x + 5y = E
$$\begin{gathered} 4\left(\frac{24}{7}\right) +5\left(\frac{113}{21}\right) =E \\ \Rightarrow E = \frac{853}{21} \\ Reqd. Line is 4x+5y=\frac{853}{21} \end{gathered}$$