Systems of Three Equations Worksheet

Practice solving systems of three linear equations using various methods.

Grade 12 Math AlgebraSystems of Three Equations

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Includes

3 Short AnswerMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.CED.A.3CCSS.MATH.CONTENT.HSA.REI.C.8

7 sections · Free to use · Printable

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Systems of Three Equations

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Solve each system of three linear equations. Show all your work clearly.

1. Solve the following system of equations:

x + y + z = 6

2x - y + 3z = 9

-x + 2y + 2z = 9

2. Find the solution to the system:

3x - y + z = -15

x + 2y - z = 1

2x + 3y - 2z = 0

3. Determine the values of x, y, and z that satisfy the system:

x + y - z = 4

3x - 2y + 4z = 11

2x + 3y + z = 13

4. Which of the following is a solution to the system:

x - y + z = 0

2x + y - z = 3

x + 2y + z = 9

(1, 2, 1)

(2, 3, 1)

(1, 3, 2)

(2, 1, -1)

5. A system of three linear equations can have exactly two solutions.

True

False

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