https://file.aiquickdraw.com/mathbot/file/1728234240087dcodihbh.jpg

The image describes a market with three types of goods and provides supply and demand equations for each good. The system of equations for supply and demand is set up to find the market equilibrium.

### Given:
Supply equations (\(Q_{s_1}, Q_{s_2}, Q_{s_3}\)):
\[
\begin{aligned}
Q_{s_1} & = x_1 - x_2 - 100 \\
Q_{s_2} & = -x_1 + x_2 - x_3 - 140 \\
Q_{s_3} & = -x_2 + 6x_3 - 100
\end{aligned}
\]

Demand equations (\(Q_{d_1}, Q_{d_2}, Q_{d_3}\)):
\[
\begin{aligned}
Q_{d_1} & = -x_1 + x_2 + x_3 + 200 \\
Q_{d_2} & = x_1 + x_2 + 200 \\
Q_{d_3} & = x_1 - 4x_3 + 100 \times 4.4 = x_1 - 4x_3 + 440
\end{aligned}
\]

The problem asks to find the equilibrium, which occurs when \(Q_s = Q_d\) for all goods.

### Steps to solve:

1. Set \(Q_{s_1} = Q_{d_1}\), \(Q_{s_2} = Q_{d_2}\), and \(Q_{s_3} = Q_{d_3}\).
2. Solve the system of equations for \(x_1\), \(x_2\), and \(x_3\).
3. Find the sum \(x_1 + x_2 + x_3\).

Let me calculate that now.The solution to the system of equations gives:

\[
x_1 = \frac{-3960}{23}, \quad x_2 = \frac{-7460}{23}, \quad x_3 = \frac{100}{23}
\]

The sum of \(x_1 + x_2 + x_3\) is:

\[
x_1 + x_2 + x_3 = \frac{-11320}{23} \approx -492.17
\]

Thus, the equilibrium sum \(x_1 + x_2 + x_3\) is approximately \(-492.17\), which differs significantly from the value "180" mentioned in the image. There might be a misunderstanding or error in the input conditions or interpretation.

Would you like more details on how this was solved, or do you have specific questions about the steps?

Here are 5 related questions:
1. What does equilibrium in supply and demand imply in economic terms?
2. Can this method be generalized to other markets with more goods?
3. What if the equations had more variables or different coefficients—how would we approach it?
4. How can changes in the demand or supply equations affect equilibrium?
5. What could cause the large negative result in this market scenario?

**Tip**: Always double-check the setup of your system before solving, especially when interpreting real-world problems like supply and demand equations.

Thị trường có 3 loại hàng hóa với hàm cung và hàm cầu lần lượt là:
Supply equations:
Q_s1 = x1 - x2 - 100
Q_s2 = -x1 + x2 - x3 - 140
Q_s3 = -x2 + 6x3 - 100
Demand equations:
Q_d1 = -x1 + x2 + x3 + 200
Q_d2 = x1 + x2 + 200
Q_d3 = x1 - 4x3 + 100 * 4.4
Find the equilibrium point where x1 + x2 + x3 equals?

Solve a system of linear equations involving supply and demand functions for three goods to find the equilibrium point in the market. This problem demonstrates key concepts in linear algebra and economics.

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