# 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!!
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!!

Have you started by dividing one equation by another?
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!!

sorry what does this symbol '^' mean?
Original post by nhsia
sorry what does this symbol '^' mean?

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

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!
Original post by TypicalNerd
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!

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

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.
(edited 3 months ago)
Original post by TypicalNerd
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!

oh yes sorry for the confusion!! its 172.8 = 10(p^3)(p^2) and -46.08 = 10(p^2)(q^3)
Original post by TypicalNerd
Have you started by dividing one equation by another?

Yeah I attempted to do that and got -3.75 = (p)(q^-1)

I'm not sure how to eliminate the p or q though.
Original post by poppjngcandy
Yeah I attempted to do that and got -3.75 = (p)(q^-1)

I'm not sure how to eliminate the p or q though.

If you multiply both sides of that by q, what do you get and why might it be useful?
Original post by TypicalNerd
If you multiply both sides of that by q, what do you get and why might it be useful?

Ohhh I think I see now!

You get p = -3.75q

You could then substitute that into either equation to solve for q and p? I got q = 0.8 and p = 3
Original post by poppjngcandy
Ohhh I think I see now!

You get p = -3.75q

You could then substitute that into either equation to solve for q and p? I got q = 0.8 and p = 3

Almost. Your method was right, but one of your answers should be negative.