Linear Systems 3x3 Worksheets Grade 12

Algebra

Solve systems of linear equations with three variables

Each printable worksheet below is a full page of practice problems and comes with an answer key that explains how to solve every problem, step by step. Open a worksheet and use the Print / Save as PDF button to download it.

Worksheet 1

8 problems
  1. Solve: 4x + 2y - 3z = 12, x - 5y + 2z = -8, 3x + y + 4z = 10
  2. 2x + y - z = 5, x - 2y + z = -5, 3x + y + 2z = 10
  3. Solve: 3x + y - z = 5, x - 3y + 2z = -7, 2x + y + z = 7

…and 5 more problems

Open & Print Worksheet 1

Worksheet 2

8 problems
  1. 3x + y - 5z = 7, x - 3y + z = -5, 5x - y + 3z = 11
  2. x + y + z = 8, 2x - y + z = 7, x - 2y + 2z = 4
  3. Liam is tracking his weekly earnings from three different jobs: tutoring, dog walking, and yard work. This week, he earned 3 times as much from tutoring as from dog walking, and his yard work earnings were $7 more than his dog walking earnings. The total amount he earned from all three jobs was $47. How much did Liam earn from dog walking?

…and 5 more problems

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Worksheet 3

8 problems
  1. Solve: 2x + 3y - 2z = 7, x - 2y + 4z = -2, 3x + y - z = 12
  2. Olivia is mixing fruit juices for a party. She has three types: apple, orange, and pineapple. The total volume of juice is 15 liters. The apple juice volume plus twice the orange juice volume minus the pineapple juice volume equals 5 liters. Also, twice the apple juice volume plus the orange juice volume plus the pineapple juice volume equals 20 liters. How many liters of apple juice does Olivia have?
  3. Solve: 2x + 3y - z = 12, x - 2y + 3z = 9, 3x + y - 2z = 11

…and 5 more problems

Open & Print Worksheet 3

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