988 CHAPTER 9 Systems and Matrices Chapter 9 Test Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 1. 3x - y = 9 x + 2y = 10 2. 6x + 9y = -21 4x + 6y = -14 3. x - 2y = 4 -2x + 4y = 6 4. 1 4 x - 1 3 y = - 5 12 1 10 x + 1 5 y = 1 2 5. 2x + y + z = 3 x + 2y - z = 3 3x - y + z = 5 Solve each system, using the method indicated. 6. 3x - 2y = 13 4x - y = 19 (Gauss-Jordan) 7. 3x - 4y + 2z = 15 2x - y + z = 13 x + 2y - z = 5 (Gaussian elimination) 9. Ordering Supplies A knitting shop orders yarn from three suppliers in Toronto, Montreal, and Ottawa. One month the shop ordered a total of 100 units of yarn from these suppliers. The delivery costs were $80, $50, and $65 per unit for the orders from Toronto, Montreal, and Ottawa, respectively, with total delivery costs of $5990. The shop ordered the same amount from Toronto and Ottawa. How many units were ordered from each supplier? Solve each problem using a system of equations. 8. Connecting Graphs with Equations Find the equation y = ax2 + bx + c of the parabola through the given points. x y 0 2 5 10 (4, 11) (2, 3) (1, 5) Solve each system using the inverse of the coefficient matrix. 87. 5x - 4y = 1 x + 4y = 3 88. 2x + y = 5 3x - 2y = 4 89. 3x + 2y + z = -5 x - y + 3z = -5 2x + 3y + z = 0 90. x + y + z = 1 2x - y = -2 3y + z = 2
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