Give me some practice problems for equations with 2 variables 

Here are some practice problems for solving equations with two variables:

1. **Linear System:**
   \[
   \begin{cases} 
   3x + 2y = 12 \\
   x - y = 1 
   \end{cases}
   \]
   Solve for $ x $ and $ y $.

2. **Linear System:**
   \[
   \begin{cases} 
   4x - y = 9 \\
   2x + 3y = 11 
   \end{cases}
   \]
   Solve for $ x $ and $ y $.

3. **Linear System:**
   \[
   \begin{cases} 
   5x + 2y = 18 \\
   3x - y = 4 
   \end{cases}
   \]
   Solve for $ x $ and $ y $.

4. **Word Problem (Linear System):**
   Sarah buys 5 pencils and 3 erasers for $4.50. Tom buys 3 pencils and 2 erasers for $2.80. 
   Let $ x $ be the cost of a pencil and $ y $ be the cost of an eraser. Set up and solve the system of equations to find the cost of a pencil and an eraser.

5. **System with Substitution:**
   \[
   \begin{cases} 
   2x + 5y = 13 \\
   y = 3x - 2 
   \end{cases}
   \]
   Solve for $ x $ and $ y $ using substitution.

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**Tip:** For solving systems of equations, try using the **substitution** or **elimination method** depending on which makes the system easier to simplify.

Would you like details on solving any of these problems or any questions so far?

**Related Questions:**
1. What are the steps of the substitution method in solving systems of equations?
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3. What happens when a system of linear equations has no solution or infinitely many solutions?
4. Can you have systems with nonlinear equations in two variables, and how are they solved?
5. How do real-world problems translate into systems of linear equations?



Give me some practice problems for equations with 2 variables

Solve systems of linear equations with two variables using substitution or elimination. Practice problems include word problems, systems of equations, and step-by-step solutions. Ideal for students in Grades 8-10.

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