Question

For what value of p will the following pair of linear equationns have infinitely many solutions? (p-3)x+3y =p;px+py=12

Answer 1

here, a1/a2=(p-3)/p
b1/b2=3/p
c1/c2=p/12
For infinite solutions,we have
a1/a2=b1/b2=c1/c2
from 1st and 2nd terms, we get
p-3/p=3/p
p(p-3)=3p
p2-3p=3p
p2-3p-3p=0
p2-6p=0
p(p-6)=0
p=6
from 2nd &3rd terms we get
3/p=p/12
p2=3×12
p2=36
p=√36
p=6
hope this will help you