1. Systems of Multivariable Equations

2. Multivariable Systems
A multivariable system is a system that has more than two variables.
Usually, it will be x, y, and z.
These types of equations are used in 3-D applications.
We will solve these using a Matrix on your calculator.
You must learn the steps; I will not give them to you for the test.
Multivariable Systems

3. Multivariable Systems
Let’s write down the calculator steps first.
1. 2nd, Matrix
2. Arrow over to Edit, Press 1
3. Set up table size (3 X 3)
4. Enter the coefficients from each equation.
5. 2nd, Matrix
6. Arrow over to Edit, Press 2
7. Set up table size (3 X 1)
8. Enter the constants from each equation.
9. 2nd, Quit
10. Press: 2nd, Matrix, 1, x-1, 2nd, Matrix , 2, Enter
11. The answer is listed.
Multivariable Systems

4. Multivariable Systems
Let’s give it a try.
2x + y + 8z = -1
x – y + z = -2
3x - 2y – 2z = 2
(2, 3, -1)
Make sure to write the answer as an ordered triple!!
Get your rules out.
Use the sign that is in front of the number when setting up your table.
Enter in your calculator.
Make sure you memorize the steps!
Multivariable Systems

5. Multivariable Systems
Try it again:
2x – y + 3z = -1
x + y – z = 0
3x + 3y – 2z = 1
(-1, 2, 1)
Multivariable Systems

6. Multivariable Systems
What happens if one of the variables is missing?
You put in a “0”!!
x + z = 1
2x + y – z = -3
x + 2y – z = -1
(-1, 1, 2)
x + 0y + z = 1
Multivariable Systems

7. Multivariable Systems
If the system has no solution or infinitely many solutions, you will get an error.
We are not going to try and figure it out, so write No Solution.
Since you have to have a calculator to do these, you can start on your homework now.
Multivariable Systems