927 CHAPTER 9 Quiz Solve each system, using the method indicated, if possible. Chapter 9 Quiz (Sections 9.1–9.4) 1. (Substitution) 2x + y = -4 -x + 2y = 2 2. (Substitution) 5x + 10y = 10 x + 2y = 2 3. (Elimination) x - y = 6 x - y = 4 4. (Elimination) 2x - 3y = 18 5x + 2y = 7 5. (Gauss-Jordan) 3x + 5y = -5 -2x + 3y = 16 6. (Cramer’s rule) 5x + 2y = -3 4x - 3y = -30 7. (Elimination) x + y + z = 1 -x + y + z = 5 y + 2z = 5 8. (Gaussian elimination) 2x + 4y + 4z = 4 x + 3y + z = 4 -x + 3y + 2z = -1 9. (Cramer’s rule) 7x + y - z = 4 2x - 3y + z = 2 -6x + 9y - 3z = -6 Solve each problem. 10. Spending on Food In 2017, the amount spent by a typical American household on food was about $7729. For every $11 spent on food away from home, about $14 was spent on food at home. Find the amount of household spending on food in each category. (Data from U.S. Bureau of Labor Statistics.) 11. Investments A sum of $5000 is invested in three accounts that pay 2%, 3%, and 4% interest rates. The amount of money invested in the account paying 4% equals the total amount of money invested in the other two accounts, and the total annual interest from all three investments is $165. Find the amount invested at each rate. 12. Let A = c -5 2 4 -1d . Find A . 13. Evaluate 3 -1 -3 2 2 -2 -1 4 -3 53 . Use determinant theorems if desired. Find the partial fraction decomposition for each rational expression. 14. 10x + 13 x2 - x - 20 15. 2x2 - 15x - 32 1x - 121x2 + 6x + 82
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