Solving simultaneous equations takes a good deal of time and precision. Once more than four equations are involved, working out a solution via pencil and paper becomes too difficult for all but the most patient. That's when it becomes worthwhile to use graphing calculators which can solve systems of nine or more simultaneous equations. You can use a TI-84 Plus to solve systems of equations by taking advantage of the TI-84's ability to do matrix mathematics.

- Skill level:
- Moderately Easy

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## Instructions

- 1
Arrange the equations into the form "axe + by +cz = d" via addition and subtraction. Place all the variables on the left in the same order for each equation and any constants without a variable on the right of the equals sign. Note how many equations you have and how many different variables there are.

- 2
Press the "2nd" key then "MATRIX". Use the right arrow key to navigate to the "EDIT" menu and press "ENTER" to edit matrix A.

- 3
Enter the number of equations you have with the keypad and press "ENTER."

- 4
Add 1 to the number of different variables in the system of equations. Enter this number with the keypad and press "ENTER." For example, if you had the system [-4x + 2y = 8, 4x + y = -3], you would enter 3.

- 5
Input each equation into the matrix with the keypad, ignoring the variables. For example, if you had the system [-4x + 2y = 8, 4x + y = -3], you would enter the numbers {-4, 2, 8, 4, 1, -3}, pressing the "ENTER" key after each number.

- 6
Press "2nd" then "QUIT". Then press "2nd" and "MATRIX." Use the right arrow key to navigate to the "MATH" menu. Scroll down to the "rref()" function and press "ENTER."

- 7
Press "2nd" and "MATRIX." Then press the "ENTER" key twice. If the equations have a solution, your calculator will solve the equations and output the values for each variable in the right column.

#### Tips and warnings

- The "rref()" function takes its name from reduced-row echelon form, a kind of form matrices can take.
- The "Simultaneous Equation Solver" program in the resources section is much easier to use.
- Some systems do not have a unique solution.