Solving Systems with Three Variables Exercises

Example 1

Solve this system in three variables.

2x – 2z = -1

x – y + 4z = -1

7x – 2y + z = 1

Hint

Eliminate y first, because that won't be hard. Then find x and z from the resulting two variable equation. Finally, find y from one of the original equations.

Example 2

Solve this system in three variables.

3x + y – 3z = -3

-x – 2y – z = -3

x – 3y + 3z = 3

Hint

Eliminate x first, then y, to find z. Work from the two variable equation to get y, then use y and z to find x.

Example 3

Solve this system in three variables.

x + y + z = 5

x – y + z = 5

x – y – z = 5

Hint

Go eliminate y first, then z.

Example 4

Solve the system of equations.

x + y + z = 9

-x – y – z = -3

Hint

Add the first two equations together.

Example 5

Solve the system of equations.

24x + y + 8z = -6

48x + 2y + 16z = 2

Hint

Check the first and third equations first.

Solving Systems with Three Variables Exercises

Solving Systems with Three Variables Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

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