Question

find the value of p for which of the following equations have infinite solution : px+3y=3, 12x+py=6 please show the method

Answer 1

$if \: the \: lines \: are \: having \: infinitely \: many \: solutions \\ \\ then \: the \: lines \: are \: coincident \\ \\ \frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \ \\ \\ \frac{p}{12} = \frac{3}{p} = \frac{3}{6} \\ \\ \frac{p}{12} = \frac{3}{p} \\ \\ cross \: multiplication \\ \\ {p}^{2} = 12 \times 3 \\ \\ {p}^{2} = 36 \\ \\ p = \sqrt{36} \\ \\ p = 6 \\ \\ mark \: me \: as \: brainliest$