Question

(p-3)x+3y =p
Px+py=12
For what value of p have infinity many solutions

Answer 1

for infinite many solutions
$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{p - 3}{p} = \frac{3}{p} = \frac{p}{12} \\ taking \: first \: and \: second \: \\ p ^{2} - 3p = 3p \\ p ^{2} = 6p \\ p = \sqrt{6p} \\ taking \: second \: and \: third \\ 36 = p ^{2} \\ p =6 \\ now \: p = p \\ \sqrt{6p} = 6 \\ p = \frac{36}{6} \\ p = 6$


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Answer 2

for infinity , many soln. a1/a2=b1/b2= c1/c2
so 1.-p-3/p=3/p
=psq-3p = 3p
=psq =3p+3p
=psq = 6p
=p=6



hope u understand