Practice Problems

1. Solve by substitution: \( x + y = 8 \), \( x - y = 2 \)
2. Solve by elimination: \( 2x + 3y = 12 \), \( 4x - y = 10 \)
3. Solve by graphing: \( y = 2x + 1 \), \( y = -x + 4 \)
4. Word problem: The sum of two numbers is 15. One is 3 more than the other. Find the numbers.
5. Solve a 3-variable system: \( x + y + z = 9 \), \( 2x - y + z = 4 \), \( x + 2y - z = 5 \)
6. Special case: Determine if \( 3x + 2y = 6 \), \( 6x + 4y = 10 \) has a solution.
7. Mixed practice: Solve \( x - y = 3 \), \( 2x + y = 7 \)
8. Word problem: A theater sells 60 tickets. Adult $10, child $6. Total $480. Find number of adult and child tickets.
9. Solve by substitution: \( 3x + y - z = 4 \), \( x - y + 2z = 3 \), \( 2x + y + z = 5 \)
10. Graphing practice: \( y = -\frac{1}{2}x + 3 \), \( y = x - 1 \)