Systems of Multivariable Equations

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

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

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

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

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

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