Answer-
The lines are two coinciding lines or the same lines.
Solution-
The given line equations are
the first one,
[tex]\Rightarrow x-5y=0[/tex]
the second one,
[tex]\Rightarrow y+1=\dfrac{1}{5}(x+5)\\\\\Rightarrow 5y+5=x+5\\\\\Rightarrow 5y=x\\\\\Rightarrow x-5y=0[/tex]
As we know two line equations [tex]A_1x+B_1y+C_1=0[/tex] and [tex]A_2x+B_2y+C_2=0[/tex] will be,
- Parallel if, [tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}[/tex]
- Coincide if, [tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}[/tex]
- Intersect if, [tex]\dfrac{A_1}{A_2}\neq \dfrac{B_1}{B_2}[/tex]
As here,
[tex]\Rightarrow \dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}[/tex]
[tex]\Rightarrow \dfrac{1}{1}=\dfrac{-5}{-5}[/tex]
(C₁ and C₂ aren't considered as they are 0)
Therefore, the lines are two coinciding lines or the same lines.
