System of Equations with Three Variables

System of Equations with Three Variables

Read each question carefully and solve the system of equations using the most appropriate method. Show all your work for full credit.

1. Solve the following system of equations:

Equation 1: x + y + z = 6

Equation 2: 2x - y + z = 3

Equation 3: 3x + 2y - z = 8

2. Which of the following is a solution to the system:

Equation 1: x - 2y + 3z = 7

Equation 2: 2x + y + z = 4

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

3. When solving a system of three linear equations, the first step is often to eliminate one variable from two pairs of equations, resulting in a system of   equations with   variables.

4. A system of three linear equations can have one unique solution,   solutions, or no solution.

5. A system of three linear equations always has at least one solution.

6. The solution to a system of three linear equations represents the point where all three planes intersect.

7. A local bakery sells three types of cookies: chocolate chip, oatmeal, and sugar. On Monday, they sold 100 cookies total. The number of chocolate chip cookies sold was twice the number of oatmeal cookies sold. The total number of oatmeal and sugar cookies sold was 60. Set up and solve a system of three equations to find how many of each type of cookie were sold.