https://file.aiquickdraw.com/mathbot/file/1726672200695t6qvpbpn.pdf

The document you provided contains a worksheet on solving systems of equations with two variables, using various methods such as graphing, substitution, and linear combination. Additionally, there are word problems involving real-life applications of systems of equations.

### Example Problems from the Document:
1. **Graphing:**
   - Solve the system of equations like:
     \[
     \begin{aligned}
     x - y &= -4 \\
     x + y &= 4
     \end{aligned}
     \]
   - Graph both equations and find the intersection.

2. **Substitution Method:**
   - Solve the system:
     \[
     \begin{aligned}
     3x - y &= 5 \\
     x + y &= 3
     \end{aligned}
     \]
   - Substitute one equation into the other to solve for \(x\) and \(y\).

3. **Linear Combination (Elimination Method):**
   - Solve the system:
     \[
     \begin{aligned}
     4x + 3y &= 0 \\
     5x - 3y &= 27
     \end{aligned}
     \]
   - Add or subtract the equations to eliminate one variable.

4. **Word Problems:**
   - Example: 
     "You collect baseball and football cards. The collection has 360 cards, with 30 more baseball cards than twice the number of football cards. Find the number of baseball and football cards."

### Do you want detailed solutions to any specific problems from the worksheet? Let me know if you need explanations for graphing, substitution, elimination, or help with word problems.

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### Related Questions:
1. How do you graphically solve a system of linear equations?
2. What is the substitution method, and when is it best used?
3. How can the elimination method simplify solving systems of equations?
4. How do systems of equations apply to real-world problems like investment returns or phone call charges?
5. What strategies can help identify whether a system of equations has no solution, one solution, or infinitely many solutions?

### Tip:
When using the substitution method, always solve one equation for the simplest variable to minimize complex algebra during substitution.

The document you provided contains a worksheet on solving systems of equations with two variables, using various methods such as graphing, substitution, and linear combination. Additionally, there are word problems involving real-life applications of systems of equations.

Learn how to solve systems of equations with two variables using graphing, substitution, and elimination methods. The worksheet covers various algebraic techniques and includes real-life word problems. Suitable for students in Grades 9-12.

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