x1=3(x2/(-t+100))-2(x1/(t+100)) and x2=2(x1/(t+100))-3(x2/(-t+100)) and x1(t)+x2(t)=150. solve for x2 at time t=30

Let's start with the given equations:

\[
x_1 = 3\left(\frac{x_2}{-t + 100}\right) - 2\left(\frac{x_1}{t + 100}\right)
\]
\[
x_2 = 2\left(\frac{x_1}{t + 100}\right) - 3\left(\frac{x_2}{-t + 100}\right)
\]
\[
x_1(t) + x_2(t) = 150
\]

We need to find \(x_2\) at \(t = 30\).

### Step 1: Substitute \( t = 30 \)
Substituting \( t = 30 \), the equations become:
\[
x_1 = 3\left(\frac{x_2}{-30 + 100}\right) - 2\left(\frac{x_1}{30 + 100}\right)
\]
\[
x_2 = 2\left(\frac{x_1}{30 + 100}\right) - 3\left(\frac{x_2}{-30 + 100}\right)
\]
\[
x_1 + x_2 = 150
\]

Calculating \( -30 + 100 = 70 \) and \( 30 + 100 = 130 \), the equations simplify to:
\[
x_1 = 3\left(\frac{x_2}{70}\right) - 2\left(\frac{x_1}{130}\right)
\]
\[
x_2 = 2\left(\frac{x_1}{130}\right) - 3\left(\frac{x_2}{70}\right)
\]
\[
x_1 + x_2 = 150
\]

### Step 2: Solve the system of equations
Let's rewrite the system for clarity:
\[
x_1 = \frac{3}{70} x_2 - \frac{2}{130} x_1
\]
\[
x_2 = \frac{2}{130} x_1 - \frac{3}{70} x_2
\]

First, we can isolate terms involving \(x_1\) and \(x_2\). Let’s solve this system to find \(x_2\).It appears that there is no solution to this system as defined, which could suggest inconsistency in the given equations or the constraints. It’s possible that a parameter might be missing or incorrectly set, or there may be special conditions where the equations don't yield a unique solution. Would you like me to investigate further or clarify any specific part of the problem?

Here are a few questions that might help refine or expand the analysis:

1. Are there any additional constraints or corrections to the original equations?
2. Should we consider any particular assumptions or approximations?
3. Would you like to see the solution process step-by-step for insight into where inconsistencies might occur?
4. Are there any numerical values you'd like substituted to check for possible solutions?
5. Would you be interested in solutions for different values of \( t \)?

**Tip:** Double-check all values and parameters to ensure they align correctly, especially in systems with multiple variables and fractions.

x1=3(x2/(-t+100))-2(x1/(t+100)) and x2=2(x1/(t+100))-3(x2/(-t+100)) and x1(t)+x2(t)=150. Solve for x2 at time t=30.

Explore how to solve a system of dynamic equations involving x1 and x2 with respect to time (t). This problem demonstrates algebraic manipulation and substitution techniques, aimed at advanced algebra students. The final solution explores inconsistencies or missing parameters in the system. Learn the step-by-step process to check for solutions at t=30.

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