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Ch 8 Exam Review Note: These are only a sample of the type of problems you may see on the test. Anything covered in class or homework may appear on the test. Identify the system as consistent or inconsistent, and Determine whether the ordered pair is a solution of the system of equations. Remember to use alphabetical order dependent or independent. 5) x + 6y = 20 of variables. 2x + 12y = 40 6x + y = 17 1) (3, -1); 2x - 3y = 9 Answer: Consistent and dependent Answer: Yes 6) 3x = y + 3 6x - 2y = 3 2) (5, -5); -2a - 5b = 15 6a + 15b = -45 Answer: Inconsistent and independent Answer: Yes 7) -8x + 2y = -6 -4x - y = -3 Solve the system graphically. If the system has an infinite number of solutions, use set-builder notation to write the solution set. If the system has no solution, state this. 3) x - y = 2 x + y = 14 Answer: Consistent and independent Solve using the substitution method. If the system has an infinite number of solutions, use set-builder notation to write the solution set. If the system has no solution, state this. 8) 5x - 2y = -1 x + 4y = 35 Answer: (3, 8) 9) 3y + x = -7 x = 4y + 9 Answer: - 1 16 ,7 7 Solve using the elimination method. If the system has an infinite number of solutions, use set-builder notation to write the solution set. If the system has no solution, state this. 10) x + 2y = -13 2x + 2y = -14 Answer: (8, 6) 4) x = y - 3 3x = 2y Answer: (-1, -6) 11) -7x + 8y = 64 -4x - 4y = -32 Answer: (0, 8) 12) 1 1 x- y=3 3 4 2 1 x+ y=1 3 2 Answer: (6, 9) Answer: 1 21 , -5 4 Solve using any appropriate method. If the system has an infinite number of solutions, use set-builder notation to write the solution set. If the system has no solution, state this. 13) 0.1x + 0.5y = 2 0.5x - 0.1y = 1 20) Determine whether (-3, -1, 4) is a solution of the system 2x - 2y - 3z = -16 4x - 3y + 3z = 3 x + y - 5z = -24. Answer: Yes 35 45 , Answer: 13 13 21) Determine whether 6, - 11 , -4 is a solution of 2 the system 3x - 2y + 3z = 17 x + 4y - 2z = -8 2x - y + z = 8. Solve the problem. 14) The sum of two numbers is 112. The second number is three times as large as the first number. What are the numbers? Answer: 28, 84 Answer: No 15) Two angles are supplementary. One angle is 212° less than three times the other. Find the measures of the angles. Solve the system. Be sure to know all mehods! 22) x - y + z = -4 x + y + z = -2 x + y - z = -6 Answer: 98°, 82° Answer: (-5, 1, 2) 16) The speed of a current is 6 mph. If a boat travels 52 miles downstream in the same time that it takes to travel 26 miles upstream, what is the speed of the boat in still water? 23) 9x - 9y - 6z = -11 6x + 3y - 3z = 1 x - y + 2z = -3 Answer: 18 mph Answer: - 17) Don runs a charity fruit sale, selling boxes of oranges for $11 and boxes of grapefruit for $10. If he sold a total of 762 boxes and took in $8125 in all, then how many boxes of oranges did he sell? 2 2 , 1, 3 3 24) -4x - y + 9z = 37 -9x + 7z = -7 5y + z = 43 Answer: (7, 7, 8) Answer: 505 boxes 25) 3x - 4y = -3 7 6x + 2z = 2 18) A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 5% cement should he mix with 4 bags of 13.5% cement to produce a mix containing 7% cement? 2y - 4z = 4 Answer: - Answer: 13 bags 1 1 3 , ,3 2 4 Solve the system. If the system's equations are dependent or if there is no solution, state this. 26) 2x + 8y + 4z = 0 x + 4y + 2z = -28 x + y + z = -4 19) Mardi received an inheritance of $60,000. She invested part at 10% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6400. Find the amount invested at 10%. Answer: No solution Answer: $40,000 27) -3x - 4y + 2z = 25 12x + 16y - 8z = -100 -9x - 12y + 6z = 75 Answer: The equations are dependent. 2 Solve. 28) The sum of a student's three scores is 221. The first is 20 more than the second, and the sum of the first two is 8 more than twice the third. Find the student's first score. Answer: 85 29) Michael's bank contains only nickels, dimes, and quarters. There are 66 coins in all, valued at $5.35. The number of nickels is 2 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank? Answer: 9 Evaluate. 30) 42 53 Answer: 2 31) -1 1 33 Answer: -6 32) -1 -3 -3 4 -5 5 -1 2 3 Answer: -95 33) 5 2 5 5 1 2 5 1 1 Answer: 5 Solve using Cramer's rule. 34) -2x - 2y = -18 3x + 5y = 43 Answer: (1, 8) 35) 2x + 2y = 28 2x - 3y = -2 Answer: (8, 6) 3