Solving Systems of Three Variables
This worksheet focuses on solving systems of linear equations with three variables using various algebraic methods.
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Solving Systems of Three Variables
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Read each problem carefully and solve the system of three linear equations using the most appropriate algebraic method. Show all your work.
1. Solve the following system of equations:
x + y + z = 6
2y + 5z = -4
2x + 5y - z = 27
2. Find the solution (x, y, z) for the system:
x - 2y + 3z = 7
2x + y + z = 4
-3x + 2y - 2z = -10
3. When solving a system of three equations with three variables, the goal is to reduce it to a system of equations with variables, and then to a single equation with one variable.
4. The point where all three planes intersect in a 3D coordinate system is the to the system of equations.
5. A system of three linear equations with three variables can have no solution, exactly one solution, or infinitely many solutions.
True
False
6. A local theater sold 200 tickets on the first night. Adult tickets cost $10, student tickets cost $5, and child tickets cost $3. The total revenue was $1200. If the number of adult tickets sold was equal to the sum of student and child tickets, how many of each type of ticket were sold?