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(p-3)x+3y=p px+py=12

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(p-3)x+3y=p px+py=12

Posted by Payal Chatterjee 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Consider equations (p - 3)x + 3y = p
and px + py = 12
For infinitely many solutions,
{tex}\frac{p - 3}{p}{/tex} = {tex}\frac{3}{p}{/tex} = {tex}\frac{p}{12}{/tex}...........(i)
Consider, {tex}\frac{3}{p}{/tex} = {tex}\frac{p}{12}{/tex} {tex}\Rightarrow{/tex} p² = 36 {tex}\Rightarrow{/tex} p = {tex}\pm{/tex}6
For p = 6, from (i) {tex}\frac{3}{6}{/tex} = {tex}\frac{3}{6}{/tex} = {tex}\frac{6}{12}{/tex}, true
For p = -6, from (i) {tex}\frac{-9}{-6}{/tex} = {tex}\frac{3}{-6}{/tex} = {tex}\frac{-6}{12}{/tex}, false.
Hence, for p = 6, pair of linear equations has infinitely many solutions.

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CBSE > Class 10 > Mathematics