https://r2.erweima.ai/mathbot/image/1726372687969mpheved8.jpg

The image contains a set of exercises about solving systems of linear equations using different methods: substitution, equalization, and elimination (reducción).

Let's go through one of the problems using the substitution method.

### Problem 1 (Substitution Method):
\[
\begin{aligned}
1. \quad & x + y = 3 \\
         & 2x + y = 0
\end{aligned}
\]

### Steps to solve:

1. **Solve for one variable from the first equation**:
   From the equation \(x + y = 3\), solve for \(y\):
   \[
   y = 3 - x
   \]

2. **Substitute this into the second equation**:
   Substitute \(y = 3 - x\) into the second equation \(2x + y = 0\):
   \[
   2x + (3 - x) = 0
   \]

3. **Simplify and solve for \(x\)**:
   \[
   2x + 3 - x = 0
   \]
   \[
   x + 3 = 0
   \]
   \[
   x = -3
   \]

4. **Substitute \(x = -3\) into the expression for \(y\)**:
   \[
   y = 3 - (-3) = 3 + 3 = 6
   \]

### Solution:
\[
x = -3, \quad y = 6
\]

Let me know if you want further details on the solution or if you'd like to tackle the other problems in the image.

Here are some related questions to expand your understanding:
1. How would the solution change if the system of equations had no solutions?
2. What are the advantages of using the substitution method over elimination?
3. Can you solve the same system using the equalization method?
4. How do you determine if a system of equations is dependent or independent?
5. How would you graphically represent the solution to this system?

**Tip**: Always verify your solutions by plugging them back into the original equations to ensure they satisfy both.

Solve the systems of linear equations using substitution, equalization, and elimination methods. Examples include equations like x + y = 3 and 2x + y = 0.

Learn how to solve systems of linear equations like x + y = 3 and 2x + y = 0 using the substitution, equalization, and elimination methods. Includes step-by-step solutions and key mathematical concepts. Suitable for students in Grades 7-10.

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