Systems of Three Equations Worksheet
This worksheet provides practice problems for solving systems of three linear equations using various methods.
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Standards
Topics
Systems of Three Equations
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Date:
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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.
True
False
6. The elimination method can be used to solve systems of three equations.
True
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?
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