Stuck on a Simultaneous Equations question

I've been struggling with this for a minute, not sure how to manipulate it..

172.8 = 10p^3q^2

-46.08 = 10p^2q^3

Any help is much appreciated!! :smile:

Reply 1

TypicalNerd

Original post by poppjngcandy

I've been struggling with this for a minute, not sure how to manipulate it..

172.8 = 10p^3q^2

-46.08 = 10p^2q^3

Any help is much appreciated!! :smile:

Have you started by dividing one equation by another?

Reply 2

nhsia

Original post by poppjngcandy

I've been struggling with this for a minute, not sure how to manipulate it..

172.8 = 10p^3q^2

-46.08 = 10p^2q^3

Any help is much appreciated!! :smile:

sorry what does this symbol '^' mean?

Reply 3

TypicalNerd

Original post by nhsia

sorry what does this symbol '^' mean?

Raised to a power of, i.e 2^2 = 4

Reply 4

nhsia

Original post by TypicalNerd

Raised to a power of, i.e 2^2 = 4

I thought that but I'm still confused. Like is it 10p^(3q + 2) or 10p + 3q^2, there's no plus/addition, idk if that's normal but it's not like any simultaneous equation i've seen :biggrin:

Reply 5

TypicalNerd

Original post by nhsia

I thought that but I'm still confused. Like is it 10p^(3q + 2) or 10p + 3q^2, there's no plus/addition, idk if that's normal but it's not like any simultaneous equation i've seen :biggrin:

I think the various terms on the right hand sides are multiplied by one another, i.e 172.8 = 10(p^3)(q^2), though it is somewhat ambiguously written in the original post as it could also be interpreted to be 172.8 = 10p^(3q)^2, which is not a very nice simultaneous equation!

Reply 6

nhsia

Original post by TypicalNerd

Yes I agree. Your first interpretation seems to make most sense (I hope for OP's sake).

Reply 7

mqb2766

Original post by poppjngcandy

I've been struggling with this for a minute, not sure how to manipulate it..

172.8 = 10p^3q^2

-46.08 = 10p^2q^3

Any help is much appreciated!! :smile:

As TypicalNerd suggested, thinking about the product and division of the two equations is really the way to go.

An arguably less elegant way would be to take logs as we're dealing with a simple product of variables. The only problem is the -46.08, but a bit of simple reasoning would give that q must be negative, so you could easily mutiply through the second equation by -1 and then solve for -q using logs. Once youve taken logs, its the usual sum and difference of simultaneous equations which youre probably more used to.