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Advanced Algebra 2
Name___________________________________ ID: 1
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8.2 Systems of Equations - 3 Variables
Date________________ Period____
Solve each system.
1) s + 3t = -8
-3r - 5s - t = -6
-5t = 10
2) -5x - 3 y = 34
y + 4z = -28
-x - 7 y + 4z = 38
3) x + 4 y = 10
-8x - 4 y - 6z = 14
8x + 6 y + 3z = -15
Worksheet by Kuta Software LLC
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4) 3a + b - 6c = 13
-a + 2b + 2c = 12
-a + 4b + 8c = 32
5) -x - 5 y + 6z = -33
3x - 3 y - 4z = -1
6x + 4 y + 8z = 6
Worksheet by Kuta Software LLC
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6) x - 3 y - 6z = 32
3x - 2 y = -8
-4x + 7 y - 4z = 22
7) 6x + 6 y - 6z = 25
10x + 2 y - 6z = 23
-4x - y - 3z = -6
8) -100x - 20 y + 20z = -21
-25x + 20 y - 20z = 21
30x + 20 y - 20z = 21
Worksheet by Kuta Software LLC
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9) The sum of three numbers is 16. The sum of twice the first number, 3 times the second number,
and 4 times the third number is 46. The difference between 5 times the first number and the
second number is 31. Find all three numbers
10) On a recent trip to the convenience store, you picked up 2 gallons of milk, 5 bottles of water, and
6 snack-size bags of chips. Your total bill was $19.00. If a bottle of water costs twice as much as
a bag of chips, and a gallon of milk costs $2.00 more than a bottle of water, how much does each
item cost?
11) In the following triangle, the degree measures of the three interior angles and two of the exterior
angles are represented with variables. Find the measure of each interior angle.
Worksheet by Kuta Software LLC
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Answers to 8.2 Systems of Equations - 3 Variables (ID: 1)
1) (6, -2, -2)
5) (1, 4, -2)
2) (-2, -8, -5)
6) (-4, -2, -5)
8) Infinitely many solutions
9) 7, 4, and 5
10) milk - $3.50, water - $1.50, chips - $0.75
3) (-6, 4, 3)
3
2
7)
, 2, 2
3
(
4) (4, 7, 1)
)
11) x = 60, y = 55, z = 65
Worksheet by Kuta Software LLC
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