https://file.aiquickdraw.com/mathbot/file/1728784926326o5l91zwu.jpg

The system of equations given in the image is:

1. \( 14x + 13y = 96 \)
2. \( 13x + 14y = 93 \)

We are tasked with finding \( x - y \).

### Step-by-step solution:

We have two equations:

\[
14x + 13y = 96 \tag{1}
\]
\[
13x + 14y = 93 \tag{2}
\]

**Step 1: Subtract Equation (2) from Equation (1)**

\[
(14x + 13y) - (13x + 14y) = 96 - 93
\]

Simplifying the left-hand side:

\[
14x - 13x + 13y - 14y = 3
\]

This simplifies to:

\[
x - y = 3
\]

Thus, \( x - y = 3 \).

---

Do you need further details or clarification on this solution?

Here are 5 related questions to expand your understanding:
1. What is the solution for \( x \) and \( y \) individually in this system?
2. How would you solve a similar system using substitution instead of elimination?
3. What would happen if the coefficients in both equations were swapped?
4. How can you verify if a solution to a system of linear equations is correct?
5. How do you represent a system of linear equations graphically?

**Tip:** When solving systems of equations, subtracting or adding the equations often eliminates one variable, making it easier to solve.

Solve the system of equations: 14x + 13y = 96 and 13x + 14y = 93, and find the value of x - y.

Learn how to solve the system of equations 14x + 13y = 96 and 13x + 14y = 93 using the elimination method to find the value of x - y. This detailed explanation covers core algebraic concepts and is suitable for students in Grades 8-10.

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