solving simultaneous equations

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pxy2d1

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i need to solve the following simultaneous equations

s^2y - sx = -1/s

s^2x + sy = 1/s

not really sure where to start
can i make x and y the subjects of each equation?
if i do this will i then be able to eliminate 1 by subtracting.
would appreciate any help ppl
thanks
 
You have two equations in three variables. This cannot be solved algebraically for a numerical answer. Sorry.

Eliz.
 
would it be possible to make x and y the subject and then eliminate one or the other leaving an equation in terms of just x or just y, still with the s terms present
 
best I could get is \(\displaystyle \L s = \frac{x-y}{x+y}\)
 
If 's' is treated as some constant, go ahead.

Where did you get these equations. They look suspicious.

I get

\(\displaystyle \L\,x = \frac{s+1}{s^{2}*(s^{2}+1)}\)

\(\displaystyle \L\,y = \frac{1-s}{s^{2}*(s^{2}+1)}\)

The Inverse LaPlace Transform would be rather simple

x ==> t + 1 - cos(t) - sin(t)

y ==> t - 1 +cos(t) - sin(t)
 
the start of the problem involved two simultaneous differential equations.
i transformed them using laplace transforms to give the two equations above.
in the example i have been trying to follow the y was eliminated and x made the subject of the equation.
The problem im having is eliminating either x or y and then making x or y the subject of the remaining equation.
once im left with an equation i want to use partial fraction expansion to find the constant terms and then use laplace transforms to find x or y.
 
Next time, don't scare the algebra students with diferential equations. :( The entire problem ALWAYS assists in more appropriate assistance.
 
pxy2d1 said:
s^2y - sx = -1/s
s^2x + sy = 1/s
Click to expand...
Add the 2 equations:
s^2 x + s^2 y - sx + sy = 0

Divide by s:
sx + sy - x + y = 0

s = (x - y) / (x + y)
or
x = (sy + y) / (1 - s)
or
y = (x - sx) / (s + 1)

Amen :idea:
 
thanks denis
could you just show me the steps to get x and y equations after dividing by s. where do the s-1 and 1 -s come from
thanks
 
pxy2d1 said:
could you just show me the steps to get x and y equations after dividing by s.
Click to expand...
If you're in differential equations, shouldn't you be familiar with the pre-calulcus algebra...?

s = (x - y)/(x + y): You're wanting to solve for "s=", so move the other terms to the other side. Then factor the "s" out of the remaining terms, and divide.

x = (sy + y)/(1 - s): You're wanting to solve for "x=", so move the other terms to the other side. Then factor the "x" out of the remaining terms, and divide.

y = (x - sx)/(s + 1): You're wanting to solve for "y=", so move the other terms to the other side. Then factor the "y" out of the remaining terms, and divide.

If you get stuck, please reply showing what you have done. Thank you.

Eliz.
 
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