Question 1

1. Solve x + 3y + z = 1
   2x – y – z = 6
   5x + y + z = 1
   

   		(1, 6, 1)
   		(1, 2, -6)
   		(2, 1, -4)
   		(-1, -2, 6)

2 points

Question 2

1. Solve x + 3y + 4z = 0
   x – 2z = 8
   y + z = 3
   

2 points

Question 3

1. Solve 4x + y + z = 1
   8x – 4y – 7z = 2
   5y – 9z = 3
   

2 points

Question 4

1. Solve x + 2y + z = 5
   2x – y + z = 4
   3x + y + 4z = 1
   

   		(5, 2, -4)
   		(1, 1, 2)
   		(2, 5, -4)
   		(5, 4, 1)

2 points

Question 5

1. Solve 2x – y – z = 3
   4x + y – 2z = 3
   -x + y + z = 1
   

   		(3, 3, 1)
   		(0, -4, 1)
   		(4, -1, 6)
   		(3, 2, 1)

2 points

Question 6

1. Solve –x + 3y + z = 9
   2x + 5y = 27
   3x + y – 2z = -18
   

   		(1, 3, -2)
   		(21, -3, 39)
   		(1, 2, -4)
   		(22, -1, 26)

2 points

Question 7

1. Solve 9x + 5y + 3z = 4
   6x + 2y + 4z = 2
   -3x + 3y – 7z = 2
   

   		(-1, 2, 1)
   		(1, -1, 0)
   		(4, 2, 2)
   		(1, 2, -5)

2 points

Question 8

1. In her wallet, Ms. Thompson has one-dollar, five-dollar, and ten-dollar bills, totally $171. She has the same number of five-dollar bills as one-dollar and ten-dollar bills put together. If she has 30 bills in all, how many bills of each denomination does she have?
   

   		11 one-dollar bills, 10 five-dollar bills, 9 ten-dollar bills
   		6 one-dollar bills, 17 five-dollar bills, 8 ten-dollar bills
   		11 one-dollar bills, 16 five-dollar bills, 8 ten-dollar bills
   		6 one-dollar bills, 15 five-dollar bills, 9 ten-dollar bills

2 points

Question 9

1. Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first number and the third number. Find the three numbers.
   

   		1st number = -6, 2nd number = 3.5, 3rd number = 2.5
   		1st number = 8, 2nd number = 4, 3rd number = 1
   		1st number = -8, 2nd number = -4, 3rd number = -1
   		1st number = 6, 2nd number = 3.5, 3rd number = -2.5

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