Systems of Three Equations

This worksheet provides practice problems for solving systems of three linear equations using various algebraic methods.

Grade 10 Math AlgebraSystems of Three Equations

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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

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

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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 = 11 -x + 2y - z = 2

2. When solving a system of three equations, the first step is often to eliminate one variable from two pairs of equations, reducing the system to two equations with variables.

3. A system of three linear equations can have a unique solution, solutions, or no solution.

4. Which of the following methods is NOT typically used to solve a system of three linear equations?

Substitution

Elimination

Graphing on a 2D plane

Matrix methods

5. Solve the system: 3x - y + 2z = 9 x + 2y - z = 4 2x - 3y + 3z = 5

6. A system of three equations always has a unique solution.

True

False

7. Find the values of a, b, and c such that the system has a solution of (1, 2, -1): ax + by + cz = 1 2ax - by + 3cz = -7 -ax + 2by - cz = 8