Practice Problems

1. Solve by substitution: \( x + 2y = 7 \), \( 3x - y = 8 \)
2. Solve by elimination: \( 2x + 3y = 12 \), \( 4x - 5y = -2 \)
3. Solve by graphing: \( y = 2x - 1 \), \( y = -x + 4 \)
4. Word problem: A store sells 50 items. Pens $1.50, notebooks $2. Total $80. Find number of pens and notebooks sold.
5. Solve 3-variable system: \( x + y + z = 10 \), \( 2x - y + z = 7 \), \( x + 2y - z = 6 \)
6. Determine if system has no solution, one solution, or infinite: \( 2x + 3y = 6 \), \( 4x + 6y = 12 \)
7. Mixed: \( x - y = 3 \), \( 2x + y = 7 \)
8. Word problem: Two numbers add to 20. One is 4 more than the other. Find numbers.
9. Solve 3-variable: \( x + y + z = 6 \), \( x - y + 2z = 5 \), \( 2x + y - z = 4 \)
10. Graphing practice: \( y = -\frac{1}{3}x + 2 \), \( y = x - 1 \)