Assessment Questions

1. Solve by substitution: \( x + y = 10 \), \( 2x - y = 3 \)
2. Solve by elimination: \( 3x + 2y = 12 \), \( 5x - y = 8 \)
3. Solve by graphing: \( y = x + 2 \), \( y = -2x + 4 \)
4. Word problem: A store sold 100 items. Shirts $10, pants $15. Total $1,250. Find number of shirts and pants sold.
5. Solve 3-variable system: \( x + y + z = 12 \), \( 2x - y + z = 7 \), \( x + 2y - z = 8 \)
6. Special case: Determine if \( 2x + 4y = 10 \), \( x + 2y = 5 \) has one solution, none, or infinite solutions.
7. Mixed practice: \( x - y = 4 \), \( 3x + y = 11 \)
8. Word problem: Two numbers sum to 45. One is twice the other. Find numbers.
9. Solve 3-variable: \( 3x + y - z = 6 \), \( x - y + 2z = 4 \), \( 2x + y + z = 8 \)
10. Graphing practice: \( y = -\frac{1}{2}x + 3 \), \( y = x - 1 \)