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en esos problemas para resolverlo trabaja los de sustitución primeros trabajas el primer ejercicio sacas X y luego el segundo ejercicio y, los de igualación trabájalos normal

Let's solve the problems in the image, focusing first on the substitution method problems, as requested. I'll walk you through the steps to solve the first problem using substitution.

### **Substitution Method**

1. **Problem 1**:
   \[
   \begin{aligned}
   1) \quad x - 2y &= 1 \quad \text{(Equation 1)} \\
   3x + y &= 3 \quad \text{(Equation 2)}
   \end{aligned}
   \]
   
   - **Step 1:** Solve Equation 1 for \( x \):
     \[
     x = 2y + 1
     \]
   
   - **Step 2:** Substitute \( x = 2y + 1 \) into Equation 2:
     \[
     3(2y + 1) + y = 3
     \]
   
   - **Step 3:** Expand and solve for \( y \):
     \[
     6y + 3 + y = 3
     \]
     \[
     7y + 3 = 3
     \]
     \[
     7y = 0 \quad \Rightarrow \quad y = 0
     \]
   
   - **Step 4:** Substitute \( y = 0 \) back into \( x = 2y + 1 \) to find \( x \):
     \[
     x = 2(0) + 1 = 1
     \]
   
   - **Solution for Problem 1:** \( x = 1 \), \( y = 0 \).

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### **Next Steps**
Do you want me to solve the second substitution problem in detail, or would you like to proceed with the problems in the "Igualación" section?

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### **Additional Practice Questions:**

1. How do you solve a system of linear equations using the elimination method?
2. Can substitution be used effectively for non-linear equations? Why or why not?
3. What are the advantages and disadvantages of using the substitution method compared to the equalization method?
4. How would you verify the solution to a system of linear equations?
5. What types of systems of equations are best suited for the substitution method?

**Tip:** When using the substitution method, always simplify the equation as much as possible before substituting the variable back into the second equation. This reduces the chances of making mistakes during the algebraic manipulation.

Learn how to solve systems of linear equations using the substitution method with a detailed step-by-step solution. This problem involves solving equations through substitution, focusing on algebraic manipulation and problem-solving skills. Suitable for high school students.

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