How Do You Solve Simultaneous Equations for Revision?

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SUMMARY

The discussion focuses on solving simultaneous equations involving energy variables and coefficients, specifically using algebraic manipulation and long division techniques. Key equations include E_{03}=E_{01}-\frac{\eta_{1}E_{02}}{\eta_{2}} and E_{1} c_1 + E_3 c_1 - E_2 c_2 = 0. Participants emphasize the importance of showing work for effective assistance and suggest treating all variables as constants except for the energy terms. The hints provided guide users through the problem-solving process, particularly in finding T and R.

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  • Understanding of simultaneous equations
  • Familiarity with algebraic manipulation techniques
  • Knowledge of energy variables and coefficients
  • Basic skills in LaTeX for mathematical notation
NEXT STEPS
  • Practice solving simultaneous equations with energy variables
  • Learn advanced algebraic techniques for long division in equations
  • Study the application of coefficients in physical equations
  • Explore LaTeX formatting for presenting mathematical work
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Students preparing for exams in physics or mathematics, educators teaching algebraic concepts, and anyone looking to improve their problem-solving skills in simultaneous equations.

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Homework Statement



Question is in the attachment, this is for revision not homework
 

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That was nasty. Lots of algebra and you'll have to use some long division. Try playing around with the formulas a bit.
 
Do you have the workings?
 
I did work out the problem, but I can't really help you unless you show some of your own work, so I just gave some hints about what to do. Try finding T by using (2) to find

E_{03}=E_{01}-\frac{\eta_{1}E_{02}}{\eta_{2}}

Then plug it into (1) and you should get the result easily. Solving for R is trickier, but I gave a good hint.
 
I would put my working but I am slow in writing latex and my exam is tomorrow, thanks for the help anyway
 
It's a lot easier than it looks, treat everything like a constant except the Es

E_{1} c_1 + E_3 c_1 - E_2 c_2 = 0

\eta _2 E_1 - \eta _2 E_3 + \eta _1 E_2 = 0

Add \frac{c_1}{\eta_2} of equation 2 to equation 1 to get you started? Solve for Es.
 
Thanks greg
 

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