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Systems of Three Equations Worksheet

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

Grade 9 Math AlgebraSystems of Three Equations
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Includes

3 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSA.CED.A.3CCSS.MATH.CONTENT.HSA.REI.C.6

Topics

AlgebraSystems of EquationsGrade 9Math
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

2y + 5z = -4

2x + 5y - z = 27

2. Find the solution to the system:

x - 2y + 3z = 7

2x + y + z = 4

-3x + 2y - 2z = -10

3. When solving a system of three equations, the goal is to find the values of x, y, and z that satisfy  .

4. A system of equations with no solution is called  .

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

T

True

F

False

6. The elimination method can be used to solve systems of three equations.

T

True

F

False

7. A local theater sold 300 tickets on opening night. Adult tickets cost $15, senior tickets cost $12, and child tickets cost $8. The total revenue was $3700. If there were twice as many adult tickets sold as child tickets, how many of each type of ticket were sold?