Question

find whether the pair of equation X + 2 Y + 5 is equal to zero and minus 3 x minus 6 Y + 1 is equal to zero have unique solution​

Answer 1

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Answer 2

$Given \: pair \: of \: equations :$

$x + 2y + 5 = 0 \: --(1) \\and \: 3x + 6y + 1 = 0 \: --(2)$

$Compare \: above \: equations \: with \\a_{1}x + b_{1}y+ c_{1} = 0 \: and \\a_{2}x + b_{2}y+ c_{2} = 0 ,\:we \:get$

$a_{1} = 1 , b_{1} = 2 , c_{1} = 5 \: and$

$a_{2} = 3 , b_{2} = 6 , c_{2} = 1$

$i) \frac{a_{1}}{a_{2}} = \frac{1}{3}$

$ii) \frac{b_{1}}{b_{2}}\\= \frac{2}{6}\\ = \frac{1}{3}$

$iii) \frac{c_{1}}{c_{2}}\\= \frac{5}{1}$

$\blue{ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}} }$

Therefore.,

$\green {The \: lines \: representing \: the }\\\green { pair \:of \: linear \: equations \: are }\\\green{ parallel\: and \: have \: no \: solutions .}$

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