How to solve this set of equations?

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In summary, the conversation discusses the solvability of a set of equations with 5 equations and 5 unknowns, with constants a, b, and c. The suggestion is made to use the Gauss-Jordan elimination algorithm to find a solution.
  • #1
KFC
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I wonder if all coupling set of equations are not solvable analytically? I have a equation set as follows

y1 = a1*y1 + c1*y2;
y2 = a2*y2+ b2*y1 + c2*y3;
y3 = a3*y3+ b3*y2 + c3*y4;
y4 = a4*y4+ b4*y3 + c4*y5;
y5 = a5*y5+ b5*y4;

a's, b's and c's are constant. So is there any way to solve these equations?
 
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  • #2
5 equations 5 unknowns. not to mention your last equation can be divided by y5
 
  • #3
dacruick said:
5 equations 5 unknowns. not to mention your last equation can be divided by y5

Sorry, some typo. I correct the equations.
 
  • #4
KFC said:
Sorry, some typo. I correct the equations.
You still have 5 equations and 5 unknowns. Look at Gauss-Jordan elimination, it's an algorithm that will spit out a solution.
 

What are the different methods to solve a set of equations?

There are several methods to solve a set of equations, such as substitution, elimination, graphing, and using matrices. Each method has its own advantages and may be more suitable for certain types of equations.

Can I use a calculator to solve equations?

Yes, calculators can be helpful in solving equations, especially when dealing with complex equations or large numbers. However, it is important to understand the steps involved in solving the equation manually as well.

Is there a specific order in which I should solve the equations?

Yes, when solving a set of equations, it is important to follow the correct order of operations, which is typically parentheses, exponents, multiplication and division (left to right), and addition and subtraction (left to right).

What should I do if I encounter fractions or decimals in the equations?

If the equations involve fractions or decimals, it is best to get rid of them by multiplying both sides of the equation by the least common denominator. This will simplify the equations and make them easier to solve.

How can I check if my solution is correct?

To check if your solution is correct, you can plug the values back into the original equations and see if they satisfy the equations. Alternatively, you can also use a graphing calculator to plot the equations and see if the lines intersect at the solution point.

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