System of Equations with Three Variables
This worksheet provides practice on solving systems of linear equations with three variables using various methods.
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System of Equations with Three Variables
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Solve each system of equations. Show all your work in the space provided.
1. Solve the following system of equations: x + y + z = 6 2x - y + z = 3 3x + 2y - z = 2
2. In the system below, if you add the first and second equations, you can eliminate the variable . x - 2y + 3z = 7 -x + y + 2z = 3 2x - 3y + z = 10
3. Which of the following is a solution to the system: x + y - z = 0 2x - y + z = 3 3x + 2y - 2z = 1
(1, 1, 2)
(2, 1, 3)
(1, 2, 3)
(3, 1, 4)
4. A system of three linear equations with three variables can have no solution, exactly one solution, or infinitely many solutions.
True
False
5. A local store sells three types of fruit: apples, bananas, and oranges. One apple, two bananas, and three oranges cost $5. Two apples, one banana, and one orange cost $3. Three apples, three bananas, and two oranges cost $7. Set up a system of three linear equations to represent this situation, where x is the cost of an apple, y is the cost of a banana, and z is the cost of an orange. You do not need to solve the system.