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The image shows a system of equations:

\[
xy = 200
\]

\[
(x - 15)(y + 3) = 200
\]

### Solving the System of Equations:

1. **Substitute** the expression for \( xy \) into the second equation.

   The first equation gives us \( xy = 200 \).

2. **Expand the second equation**:
   
   \[
   (x - 15)(y + 3) = 200
   \]
   
   Expanding this:
   
   \[
   xy + 3x - 15y - 45 = 200
   \]

3. **Substitute** \( xy = 200 \) into the expanded equation:
   
   \[
   200 + 3x - 15y - 45 = 200
   \]
   
   Simplifying:
   
   \[
   3x - 15y = 45
   \]
   
   This can be simplified further by dividing the entire equation by 3:
   
   \[
   x - 5y = 15
   \]

4. **Now, solve the two equations**:

   You now have a system:
   
   \[
   xy = 200
   \]
   
   \[
   x - 5y = 15
   \]

5. **Substitute** \( x = 5y + 15 \) from the second equation into the first equation:
   
   \[
   (5y + 15)y = 200
   \]
   
   Expanding:
   
   \[
   5y^2 + 15y = 200
   \]
   
   Divide the entire equation by 5 to simplify:
   
   \[
   y^2 + 3y - 40 = 0
   \]

6. **Solve the quadratic equation**:
   
   \[
   y^2 + 3y - 40 = 0
   \]
   
   This can be solved using the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 3 \), and \( c = -40 \).
   
   \[
   y = \frac{-3 \pm \sqrt{3^2 + 160}}{2}
   \]
   
   \[
   y = \frac{-3 \pm \sqrt{169}}{2}
   \]
   
   \[
   y = \frac{-3 \pm 13}{2}
   \]
   
   So, \( y = 5 \) or \( y = -8 \).

7. **Find the corresponding \( x \) values**:
   
   - For \( y = 5 \):
     \[
     x = 5(5) + 15 = 40
     \]
   - For \( y = -8 \):
     \[
     x = 5(-8) + 15 = -25
     \]

### Solutions:
- \( (x, y) = (40, 5) \)
- \( (x, y) = (-25, -8) \)

Would you like further details or have any questions?

### Related Questions:
1. How can you verify the solutions of a system of equations?
2. What methods other than substitution can be used to solve systems of equations?
3. How does the discriminant in the quadratic formula help determine the nature of the roots?
4. What are some real-life applications of solving systems of equations?
5. How can systems of equations be solved graphically?

### Tip:
When solving quadratic equations, always check if the equation can be factored easily before applying the quadratic formula, as factoring can often save time.

Learn how to solve the system of equations xy = 200 and (x - 15)(y + 3) = 200 with a detailed step-by-step solution. This problem covers key algebraic concepts including systems of equations, quadratic equations, and the quadratic formula. Suitable for high school students.

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