Question

for what value of p and q will the following pairs of linear equations has infinitely many solutions? 4x+5y=2;(2p+7q)x+(p+8q)y=2q-p+1

Answer 1

what are your thoughts on how to do this?

Answer 2

on how to do it

Answer 3

do you know under what conditions a pair of linear equations has infinitely many solutions?

Answer 4

yes

Answer 5

could you explain please?

Answer 6

(I am trying to guide you to how to solve this question)

Answer 7

a1/a2=b1/b2=c1/ c2

Answer 8

perfect! :)

Answer 9

so if the coefficients of the second equation are a multiple of the coefficients of the first equation, then the two equations are not linearly independent and will therefore have an infite number of solutions.

Answer 10

so you can start by saying that all the coefficients of the second equation must some multiple of the first equation - lets cal this multiple 'k'

this gives us the following 3 equations to solve:\[\begin{align}
2p+7q&=4k\tag{1}\\
p+8q&=5k\tag{2}\\
2q-p+1&=2k\tag{3}\end{align}\]make sense?

Answer 11

yah got it

Answer 12

hopefully you can solve from here?

Answer 13

thanks a lot

Answer 14

yw :)