Solving Systems of Equations with Three Variables

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

Grade 9 Math AlgebraSystem of Equations with Three Variables

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2 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSA.REI.C.8

Topics

AlgebraSystems of EquationsThree VariablesGrade 9

6 sections · Free to use · Printable

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Solving Systems of Equations with Three Variables

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Solve each system of three linear equations with three variables. 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 - 2y + z = 12 x + 3y - z = 1 2x - y + 2z = 10

3. When solving a system of three equations with three variables, the goal is to find the point of of the three planes.

4. The first step in the elimination method for three variables is to eliminate one from two pairs of equations.

5. A system of three linear equations with three variables always has exactly one unique solution.

True

False

6. Substitution can be used to solve systems of three variables, but it often requires more algebraic manipulation than elimination.

True

False

7. A chemist needs to mix three solutions of different concentrations. Solution A is 10% acid, Solution B is 20% acid, and Solution C is 30% acid. She wants to make 100 liters of a mixture that is 22% acid. She also wants the amount of Solution C to be twice the amount of Solution A. How many liters of each solution should she use?