https://file.aiquickdraw.com/mathbot/file/17285454557341hop4age.jpg

The given system of linear equations is:

\[
\begin{aligned}
x_1 + x_2 &= 1 \\
x_2 + x_3 &= 4 \\
x_3 + x_4 &= -1 \\
x_4 &= -4
\end{aligned}
\]

### Step-by-step solution:

1. **From the last equation**:
   \[
   x_4 = -4
   \]
   
2. **Substitute \(x_4 = -4\) into the third equation**:
   \[
   x_3 + (-4) = -1 \quad \Rightarrow \quad x_3 = -1 + 4 = 3
   \]

3. **Substitute \(x_3 = 3\) into the second equation**:
   \[
   x_2 + 3 = 4 \quad \Rightarrow \quad x_2 = 4 - 3 = 1
   \]

4. **Substitute \(x_2 = 1\) into the first equation**:
   \[
   x_1 + 1 = 1 \quad \Rightarrow \quad x_1 = 1 - 1 = 0
   \]

### Final solution:
\[
\begin{aligned}
x_1 &= 0 \\
x_2 &= 1 \\
x_3 &= 3 \\
x_4 &= -4
\end{aligned}
\]

If you need more details or have any questions, feel free to ask!

Here are 5 related questions to expand on this topic:
1. How do you represent a system of equations in matrix form?
2. What methods can be used to solve a system of linear equations?
3. What are the advantages of using matrix methods over substitution?
4. How do you determine if a system of equations has no solution or infinite solutions?
5. Can a system of linear equations be inconsistent?

**Tip:** When solving systems of equations, always check for dependent equations that might indicate infinite solutions or inconsistency.

Solve the system of linear equations: x1 + x2 = 1, x2 + x3 = 4, x3 + x4 = -1, x4 = -4.

Learn how to solve the system of linear equations with detailed steps: x1 + x2 = 1, x2 + x3 = 4, x3 + x4 = -1, x4 = -4. This solution uses the substitution method and explores key concepts in Linear Algebra, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation