Math, asked by rasmitapadhy640, 6 months ago

the equation x/2+y 1/5=0 and 4x+8y+8/5=0represent a pair of coincident lines

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Answered by Mihir1001

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Two linear equations in two variables :

$\large{ \frac{1}{2} x + y + \frac{1}{5} = 0}$
$\large{4x + 8y + \frac{8}{5} = 0}$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: prove :-}}}}$

These pair of equations represent a pair of coincident lines.

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Linear Equations in Two Variables

$\LARGE{\underline{\mathtt{\textcolor{blue}{Proof :-}}}}$

We have,

$\large{ \frac{1}{2} x + y + \frac{1}{5} = 0}$
$\large{4x + 8y + \frac{8}{5} = 0}$

which are of the form :

$\large{a_1x + b_1y + c_1 = 0}$
$\large{a_2x + b_2y + c_2 = 0}$

where,

$\large{a_1 = \frac{1}{2} \: , \: b_1 = 1 \: , \: c_1 = \frac{1}{5} }$
$\large{a_2 = 4 \: , \: b_2 = 8 \: , \: c_1 = \frac{8}{5} }$

Now,

$\large{ \frac{a_1}{a_2} = \frac{1/2}{4} = \frac{1}{8} }$

$\large{ \frac{b_1}{b_2} = \frac{1}{8} = \frac{1}{8} }$

$\large{ \frac{c_1}{c_2} = \frac{1/5}{8/5} = \frac{1}{8} }$

Thus,

$\large{ \frac{a_1}{a_2} = \frac{b_2}{b_2} = \frac{c_1}{c_2} }$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

Hence, these two equations represent a pair of coincident lines.

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the equation x/2+y 1/5=0 and 4x+8y+8/5=0represent a pair of coincident lines​

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Hence, these two equations represent a pair of coincident lines.

the equation x/2+y 1/5=0 and 4x+8y+8/5=0represent a pair of coincident lines