Question

x/2 +y +2/5 =0 ; 4x+8y+5/16=0 does the following pair of equation represent a pair of coincident lines

Answer 1

pls refer to the attachment

it is parallel.

thanks

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Answer 2

Answer:

The given pair of equation does not represent a pair of coincident lines.

Step-by-step explanation:

Given two lines

$\frac{x}{2}+y+\frac{2}{5}=0\\\\4x+8y+\frac{5}{16}=0$

$\frac{x}{2}+y+\frac{2}{5}=0$

⇒ $y=\frac{-x}{2}+(-\frac{2}{5})$    →   (1)

Here, the slope is \frac{1}{2} and intercept i.e cut y-axis at -\frac{2}{5}

$4x+8y+\frac{5}{16}=0$

⇒ $y=\frac{1}{8}[-4x-\frac{5}{16}]$

⇒ $y=\frac{-x}{2}+(\frac{-5}{128})$   →   (2)

The given two lines has same slope but different intercept i.e these two lines cut y- axis at different points, which shows that these lines are not coincident. These lines are parallel shown in graph also in attachment.

Hence, given pair of equation does not represent a pair of coincident lines.