Solving Systems of Three Variables

Solving Systems of Three Variables

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.

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?