About solving simultaneous equation

gabrielwong1991

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Hi, could anyone get the answer for this one?

\(\displaystyle 0.7\, \sqrt{100\, -\, p\,} \, +\, 0.3\, \sqrt{36\, -\, p\, +\, B\,}\, -\, 1\, =\, \overline{u}\, =\, 7.8\)

\(\displaystyle 0.7\, \sqrt{100\, -\, p\,} \, +\, 0.3\, \sqrt{36\, -\, p\, +\, B\,}\, -\, 1\, =\, 0.3\, \sqrt{100\, -\, p\,}\, +\, 0.7\, \sqrt{36\, -\, p\, +\, B\,}\)

Basic algebra yields \(\displaystyle p\, \approx\, 8.8,\, B\, \approx\, 22.5\)

It would be great if you provide steps, I just cant get the answer the teacher gave us...

Many thanks!
 
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Hi, could anyone get the answer for this one?

\(\displaystyle 0.7\, \sqrt{100\, -\, p\,} \, +\, 0.3\, \sqrt{36\, -\, p\, +\, B\,}\, -\, 1\, =\, \overline{u}\, =\, 7.8\)

\(\displaystyle 0.7\, \sqrt{100\, -\, p\,} \, +\, 0.3\, \sqrt{36\, -\, p\, +\, B\,}\, -\, 1\, =\, 0.3\, \sqrt{100\, -\, p\,}\, +\, 0.7\, \sqrt{36\, -\, p\, +\, B\,}\)

Basic algebra yields \(\displaystyle p\, \approx\, 8.8,\, B\, \approx\, 22.5\)

It would be great if you provide steps, I just cant get the answer the teacher gave us...

Many thanks!
Please show us your attempt or how you even started the solution.
 
Last edited by a moderator:
Hi, could anyone get the answer for this one?

\(\displaystyle 0.7\, \sqrt{100\, -\, p\,} \, +\, 0.3\, \sqrt{36\, -\, p\, +\, B\,}\, -\, 1\, =\, \overline{u}\, =\, 7.8\)

\(\displaystyle 0.7\, \sqrt{100\, -\, p\,} \, +\, 0.3\, \sqrt{36\, -\, p\, +\, B\,}\, -\, 1\, =\, 0.3\, \sqrt{100\, -\, p\,}\, +\, 0.7\, \sqrt{36\, -\, p\, +\, B\,}\)

Basic algebra yields \(\displaystyle p\, \approx\, 8.8,\, B\, \approx\, 22.5\)
Is there supposed to be a second "equals" sign in the first "equation"? Are you given any information about \(\displaystyle \overline{u}?\)

I just cant get the answer the teacher gave us...
If you were given a worked solution, please provide this, and state specifically where things stop making sense to you. If, by "answer", you mean the numerical bit, then what happened to the \(\displaystyle \overline{u}?\) Thank you! ;)
 
So for the first equation, I squared both sides so the square root cancels out. can I do that?

0.7^2(100-P)^1/2 + 0.3^2(36-P+B)^1/2=8.8^2

0.49(100-P)+0.09(36-P+B)=77.44?

It doesnt comes with steps just the answer on the bottom part...

Maybe let me take a photo of my attempt...
 
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It might look easier if you let
\(\displaystyle x = \sqrt{100\, -\, p\,}\)
and
\(\displaystyle y = \sqrt{36\, -\, p\, +\, B\,}\)
and then look at it as simultaneous equations.

EDIT: Oh, and notice that that second equation can be written as
0.4 x - 0.4 y = 1
 
I got it now! Its the positive and negative sign that messed me up! Careless mistakes! Sorry guys thanks for your time!:p
 
So for the first equation, I squared both sides so the square root cancels out. can I do that?

0.7^2(100-P)^1/2 + 0.3^2(36-P+B)^1/2=8.8^2

0.49(100-P)+0.09(36-P+B)=77.44?

It doesnt comes with steps just the answer on the bottom part...

Maybe let me take a photo of my attempt...
I have a bit to say about your work so far.
You wrote 0.49(100-P)+0.09(36-P+B)=77.44?

You think that (a+b)^2 = a^2 + b^2. Let's accept that as true for a moment.

you computed (.7)^2 to get .49. But you never squared the result like you did to (100-P)^1/2

if you want to square a product you must square each factor. For example [(3)^2*(4)]^2 = [9*4]^2 = 9^2 * 4^2 =81*16= 1296, not 3^2 * 4^2 = 144

Now consider (3+4)^2. well this is 7^2 which is 49. While 3^2 + 4^2 = 9 + 16 = 25. So (a+b)^2 is not a^2 + b^2

You think that you squared the left side, fine but you did not square the right side. Just because the right hand side is something squared you still have to square it. For example, we know that 4 = 2^2. If we square both sides we do NOT get 4^2 =2^2 because that says 16 = 4 and that is not true. You must square the 2^2 and get 16.

Hints have already been given how to proceed. Go over the mistakes you made until you understand them. Just think of things like 2^2 as a number and maybe you need to square it.
 
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Yup Jomo you are right I always have doubt on the square bit and that clear things up for me! Thanks

Sometimes when you don't do maths for a while it gets rusty... - Haven't touch maths for 2 years now!
 
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If your teacher was showing how to solve 2 simultaneous equations
and made up those in order to demonstrate, then he/she needs
a stiff kick you-know-where :shock:
Maybe for extra credit and to get students to think 'outside the box':
\(\displaystyle x = \sqrt{100\, -\, p\,}\)
\(\displaystyle y = \sqrt{36\, -\, p\, +\, B\,}\)

0.7 x + 0.3 y - 1 = \(\displaystyle \overline{u}\) = 7.8
0.7 x + 0.3 y - 1 = 0.3 x + 0.7 y
translates to
0.7 x + 0.3 y = 8.8
0.4 x - 0.4 y = 1
or multiplying the second equation by 0.3/0.4 = 0.75
0.7 x + 0.3 y = 8.8
0.3 x - 0.3 y = 0.75
Adding the two equations together, solving for x and back solving for y gives
x = 9.55
y = 7.05
x2 = 100 - p
y2 = 36 - p + B
or
p = 100 - x2 = 8.7975
B = y2 + p - 36 = 22.5
 
If your teacher was showing how to solve 2 simultaneous equations
and made up those in order to demonstrate, then he/she needs
a stiff kick you-know-where :shock:
I agree only somewhat since he/she still will be in the classroom. Personally I am against the death penalty but then again maybe .....
 
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