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Equation Solving

Hi I need help solving these equations for A1A_1 and A2A_2. I'm probably being stupid, but am having trouble working any similar questions out. Any help is much appreciated. :smile:

1A1−p1λ=0\frac {1}A_1 - p_1\lambda = 0



3A2−p2λ=0\frac {3}A_2 - p_2\lambda = 0



6p1−p1A1−p2A2=06p_1 - p_1A_1 - p_2A_2 = 0
Original post by Crazy Paving
Hi I need help solving these equations for A1A_1 and A2A_2. I'm probably being stupid, but am having trouble working any similar questions out. Any help is much appreciated. :smile:

1A1−p1λ=0\frac {1}A_1 - p_1\lambda = 0



3A2−p2λ=0\frac {3}A_2 - p_2\lambda = 0



6p1−p1A1−p2A2=06p_1 - p_1A_1 - p_2A_2 = 0

Do you need to solve them simultaneously and is it ok to have an answer in terms of p1p_1 and p2p_2?

If so, rearrange the first equation for lambda, then substitute the result into the second equation in place of that lambda. Next, rearrange the new equation for A1A_1 (Or A2A_2, if you want to) and then substitute this result into the third equation and solve for A2A_2 (or A1A_1 if you chose to rearrange for A2A_2 in the first step). To get A1A_1, substitute the previous result into the third equation in place of A2A_2 and solve for A1A_1.

We're not supposed to type out full solutions so that's as much help as I can give without you showing some working. Hope that helps.
(edited 13 years ago)
re-arrange the first equation to find p1. do the same with the second to find p2. plug these new values of p1 and p2 into the third equation. The A2's cancel, and you can take 1/landa out. then solve for A1 (i get 3/2)

i can't see an obvious way for A2..
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Crazy Paving
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Original post by Farhan.Hanif93
Do you need to solve them simultaneously and is it ok to have an answer in terms of p1p_1 and p2p_2?

If so, rearrange the first equation for lambda, then substitute the result into the second equation in place of that lambda. Next, rearrange the new equation for A1A_1 (Or A2A_2, if you want to) and then substitute this result into the third equation and solve for A2A_2 (or A1A_1 if you chose to rearrange for A2A_2 in the first step). To get A1A_1, substitute the previous result into the third equation in place of A2A_2 and solve for A1A_1.

We're not supposed to type out full solutions so that's as much help as I can give without you showing some working. Hope that helps.


Yeah, A2A_2 was in terms of p1p_1 and p2p_2 but A1A_1 was an actual number (fraction). I tried your approach but ended up just confusing myself again (probably just me and my dusty brain). Thanks for the help though! :smile:

Original post by future marine 1991
re-arrange the first equation to find p1. do the same with the second to find p2. plug these new values of p1 and p2 into the third equation. The A2's cancel, and you can take 1/landa out. then solve for A1 (i get 3/2)

i can't see an obvious way for A2..


It took me a while, but I finally got there. The answer was 32\frac{3}2 and thank you very much for your help. It had been bugging me for ages, and I'll try this approach in future with any problems like this. Cheers! :yy:

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