https://file.aiquickdraw.com/mathbot/file/17259187787368bvq2cxi.jpg

The system of linear equations shown in the image is:

1. \( 5x - 2y = 29 \)
2. \( 3x + 4y = 33 \)

Let's solve this system using either substitution or elimination. I'll use the elimination method.

### Step-by-Step Solution:

1. **Multiply the first equation by 2** to eliminate the \(y\)-terms:

   \[
   2(5x - 2y) = 2(29)
   \]
   \[
   10x - 4y = 58
   \]

2. **Add the two equations together** to eliminate \(y\):

   \[
   (10x - 4y) + (3x + 4y) = 58 + 33
   \]
   \[
   13x = 91
   \]

3. **Solve for \(x\)**:

   \[
   x = \frac{91}{13} = 7
   \]

4. **Substitute \(x = 7\) into one of the original equations**, let's use \(3x + 4y = 33\):

   \[
   3(7) + 4y = 33
   \]
   \[
   21 + 4y = 33
   \]
   \[
   4y = 12
   \]
   \[
   y = \frac{12}{4} = 3
   \]

### Solution:

The solution to the system is \(x = 7\) and \(y = 3\).

---

Would you like further details on any step? Here are 5 related questions you might find useful:

1. How can the substitution method be used for solving this system?
2. What is the graphical interpretation of this system of equations?
3. How do you check if the solution is correct?
4. What are the advantages of using the elimination method?
5. Can systems of equations always be solved using elimination?

**Tip:** Always check your solution by substituting the values of \(x\) and \(y\) into the original equations.

Solve the system of linear equations: 5x - 2y = 29 and 3x + 4y = 33

Learn how to solve the system of linear equations 5x - 2y = 29 and 3x + 4y = 33 using the elimination method. This solution provides a detailed, step-by-step approach suitable for students in Grades 9-11.

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