System of Equations: Solving U & V with Polynomials

In summary, the problem involves solving for U and V in two equations with multiple variables. The solutions are U=(s+1)/s^2 and V=(2s+1)/s^2. The approach involves simplifying the equations and using elimination to eliminate one variable in order to solve for the other.
  • #1
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Homework Statement



sU-1+U-V=0
sV-2-U+V=(2/s)

Homework Equations


N/A

The Attempt at a Solution


the solutions are
U=(s+1)/s^2

V=(2s+1)/s^2

but I just keep getting complicated polynomials that I don't seem to be able to factor.

If someone could show me how this particular one was done and what a general approach is I would greatly appreciate it.
 
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  • #2
I was able to get the answers you posted. It may help to "clean" up the equations so that there is only one U and one V shown in each on the LHS, like this:

[tex]\begin{aligned}
(s+1)U - V &= 1 \\
-U + (s+1)V &= (2/s) + 2
\end{aligned}[/tex]

I used elimination by multiplying eq. 1 by s+1 and adding to eq. 2 to eliminate the V. In any event you have to show your work first, so either show us what you've got or try what I did, and we'll check it for you.
 

FAQ: System of Equations: Solving U & V with Polynomials

How do you solve a system of equations with polynomials?

To solve a system of equations with polynomials, you can use the substitution method or the elimination method. In the substitution method, you solve for one variable in one of the equations and then substitute that value into the other equation. In the elimination method, you manipulate the equations to eliminate one variable and then solve for the remaining variable.

Can you explain the difference between solving for U and V in a system of equations with polynomials?

When solving for U and V in a system of equations with polynomials, you are essentially solving for two different variables. U and V are independent variables that can have different values and are not related to each other. Solving for U and V allows you to find the specific values for each variable that satisfy both equations in the system.

What do you do if the system of equations has more than two variables?

If the system of equations has more than two variables, you will need to use additional equations to solve for all the variables. This means you will need to have an equal number of equations and variables in order to solve the system. You can use the same methods of substitution or elimination, but you may need to repeat the process multiple times to solve for all the variables.

Can you solve a system of equations with polynomials using a graphing calculator?

Yes, you can solve a system of equations with polynomials using a graphing calculator. Most graphing calculators have a built-in function for solving systems of equations. You can enter the equations into the calculator and it will provide you with the solutions for the variables. However, it is still important to understand the concepts behind solving systems of equations in order to use the calculator effectively.

What is the importance of solving systems of equations with polynomials in real life?

Solving systems of equations with polynomials is important in real life because it allows us to find the values of multiple variables that satisfy a set of equations. This is useful in a variety of fields, such as engineering, physics, and economics, where systems of equations are used to model real-life situations. By solving these systems, we can make predictions and solve real-world problems.

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