https://file.aiquickdraw.com/mathbot/file/1726133756515pvl93t9j.jpg

I see you've uploaded an image of a system of linear equations (SPLDV) solution. Let's break down the process:

1. The given system of equations is:
   - \( 4x - y = 13 \) 
   - \( 2x + 3y = 19 \)

2. The steps show that you multiplied the second equation by 4 to eliminate \(x\), which results in:
   - \( 8x - 2y = 26 \) (from multiplying the first equation by 2)
   - \( 8x + 12y = 76 \) (from multiplying the second equation by 4)

3. Then, you subtracted the two equations:
   - \( (8x - 2y) - (8x + 12y) = 26 - 76 \)
   - This simplifies to \( -14y = -50 \), so \( y = \frac{50}{14} = \frac{25}{7} \).

4. You substituted \( y = \frac{25}{7} \) back into the first equation to solve for \(x\):
   - \( 4x - \frac{25}{7} = 13 \)
   - Multiplying through by 7 gives \( 28x - 25 = 91 \), so \( 28x = 116 \), and finally \( x = \frac{116}{28} = \frac{29}{7} \).

5. Therefore, the solution is \( x = \frac{29}{7} \) and \( y = \frac{25}{7} \), as shown at the end.

Yes, the solution is correct. Let me know if you'd like more detailed clarification on any of the steps.

Here are five related questions:
1. How would the solution change if both equations were multiplied by different numbers initially?
2. Can this system of equations be solved using the substitution method?
3. What are some applications of solving systems of equations in real life?
4. How can you verify if your solution is correct?
5. What happens if both equations are dependent (have infinite solutions)?

**Tip:** Always double-check your solution by substituting the values of \(x\) and \(y\) back into the original equations to verify correctness.

Learn how to solve the system of linear equations 4x - y = 13 and 2x + 3y = 19 using the elimination method. This detailed step-by-step solution includes multiplying equations to eliminate variables and solve for both x and y. Suitable for Grade 9-10 students.

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