Finding variables: (y/1-y) = 1.99*(x/1-x) - 1.8*10^-6

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fvitchard

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Jan 29, 2007
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Ok, these may seem pretty easy - but its been a LONG time since I've been in school and had to play around with equations. 2 questions I need help with...

The first, I've essentially boiled down a problem to a linear equation in which I have to plot different values of x and y. However, it isn't an exact y=mx+b deal. The equation is:

(y/1-y) = 1.99*(x/1-x) - 1.8*10^-6

I'm having trouble remembering how to break the (y/1-y) and the (x/1-x). Basically I need a way to be able to assign a value to either x or y and solve for the other so I can plot them.

The second question is very similar in that I can't remember how to break out the (1/1-x) from an equation. The equation is:

333*(0/1-0) + 5.18*(y/1-y) = 333*(x/1-x) + 5.18(0.02/1-0.02)

I need to get that equation into a form that would allow me to plug a value for y in to find a value for x. Also if there is a way to do the reverse and plug in a value for x to obtain a value for y, that would help too.

Any help you can provide would be MUCH appreciated!

Thanks!
 
For the first problem, I started with the following equation:

V' * (y1/1-y1) + L' * (xn/1-xn) = V' * (yn/1-yn) + L' * (xo/1-xo)

I divided that by V' and rearranged to the following:

(yn/1-yn) = [(L'/V') * (xn/1-xn)] + [(y1/1-y1) - (L'/V')*(xo/1-xo)]

Since yn and xn are the ordinate and the abrissa on the line, I dropped the subscripts to yield the following equation:

(y/1-y) = [(L'/V')*(x/1-x)] + [(y1/1-y1) - (L'/V')*(xo/1-xo)]

where I substituted the know values for L', V', y1, and xo to obtain the formula in which I had a question on:

(y/1-y) = 1.99*(x/1-x) - 1.8*10^-6


The second question uses a similar preliminary basic equation in the first part:

L' * (xo/1-xo) + V' * (y/1-y) = L' * (x/1-x) + V' * (y1/1-y1)

I substituted known values of L', V', xo, and y1. If I can break this equation down to y = and conversely to x = then I can substitute experimental values of x in to find y and vice versa.

Thanks again for the help!
 
Am I in the correct forum for this question? If so, any help offered would be much appreciated.

Thanks!
 
YOUR equation: (y/1-y) = 1.99*(x/1-x) - 1.8*10^-6

I assume you mean: (y/(1-y)) = 1.99*(x/(1-x)) - 1.8*10^-6
else the left side = 0 since y/1 - y = 0, and y is can't be "solved for".

Make your life easier: a = 1.99, b = 1.8*10^-6 ; then equation becomes:
(y / (1 - y)) = a(x / (1 - x)) - b
(y / (1 - y)) - ax / (1 - x) + b = 0

Apply LCM (1 - x)(1 - y):
y(1 - x) - ax(1 - y) + b(1 - x)(1 - y) / ((1 - x)(1 - y)] = 0

Any fraction = 0 means numerator = 0; so:
y(1 - x) - ax(1 - y) + b(1 - x)(1 - y) = 0

y - xy - ax + axy + b - b(1 - x - y + xy) = 0
y - xy - ax + axy + b - b + bx + by - bxy = 0
isolating x:
bxy + xy + ax - axy - bx = by + y
x(by + y + a - ay - b) = y(b + 1)

x = y(b + 1) / (by + y + a - ay - b)

Now substitute a and b back in...

You can isolate y similarly.

Check my work: not guaranteed to be typoless or errorless :wink:
 
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