# Solve x+y=5 & x^x+y^y=31 | Get Help Here

• abia ubong
In summary, the conversation is about a simultaneous equation (x+y=5, x^x+y^y=31) and the poster is looking for a solution. It is mentioned that this question has been posted before and the initial equation has been solved by the respondent but the second equation cannot be solved by elementary functions. However, it is suggested that the solutions for x= 3, y= 2 and x= 2, y= 3 are probably the only ones and can be checked easily.
abia ubong
hey i need help with this its a simul eqn ,here it is ,
x+y=5,x^x+y^y=31.any help will be appreciated

abia ubong said:
hey i need help with this its a simul eqn ,here it is ,
x+y=5,x^x+y^y=31.any help will be appreciated
Why do I feel I have seen this before?

(2,3)

The Bob (2004 ©)

can i get a solution plssssssssssssssss

This is, after all, the second time you have posted this question: all I can do is give the same answer I did before: from x+ y= 5, y= 5- x so the second equation can be written xx+ (5-x)5-x= 31. That equation cannot be solved (for arbitrary right hand side) by any elementary functions. It is possible that such an equation can be solved by the "Lambert W function".

However, as was explained the last time this was posted, in this particular problem,
33+ 22= 31 so x= 3, y= 2 and x= 2, y= 3 are solutions. They are probably the only solutions. It shouldn't be too difficult to check that.

## 1. What is the solution to the equations x+y=5 and x^x+y^y=31?

The solution to these equations is x=3 and y=2. This can be found by substituting y=5-x into the second equation and solving for x.

## 2. How do you solve a system of equations with two variables?

To solve a system of equations with two variables, you must first isolate one variable in one of the equations. Then, substitute that value into the other equation and solve for the remaining variable. Finally, plug the value of the remaining variable into the first equation to find the value of the first variable.

## 3. Can these equations be solved using algebraic methods?

Yes, these equations can be solved using algebraic methods. By isolating one variable in one of the equations and substituting it into the other equation, we can solve for the remaining variable.

## 4. Are there any other methods for solving these equations?

Yes, these equations can also be solved using graphical or numerical methods. Graphing the two equations on a coordinate plane and finding the intersection point can give the solution. Using a calculator or computer program to solve the equations numerically can also provide the solution.

## 5. Can you explain the reasoning behind the solution to these equations?

The solution to these equations can be found by considering the properties of exponents and using algebraic manipulation. By isolating one variable and substituting it into the other equation, we can eliminate one variable and solve for the remaining variable. This solution satisfies both equations, making it the correct solution.

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