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How to Solve Simultaneous Equations With a Ti 89

by Andy Pasquesi, Demand Media

    From Algebra I to the SAT Math and beyond, the ability to solve simultaneous first-order (i.e. no exponents) equations can be a lifesaver. While solving for two variables (x,y) is doable, solving for three variables (x,y,z) can be very time consuming. Plus, more variables means a greater risk of careless mistakes. Luckily, the TI-89 calculator can make quick work of three-variable simultaneous equations, and this article will take you through the process step-by-step.

    Getting The Coefficients

    Step 1

    Determine all of the variables used in the equations (x, y, z)

    Step 2

    Rearrange each equation so that it's in the form "ax + by + cz = d" where a, b, c & d are constants. Also, if one of the variables doesn't appear in one of the equations, set its coefficient to "0", i.e. "6y + 4x = 15" would be written "4x + 6y + 0z = 15."

    Step 3

    On a piece of scratch paper, list the equations in a column, one on top of the other. Make sure that the variables in each equation are in the same order, i.e. first "x," then "y," then "z."

    Step 4

    Erase or scratch out all of the variables, leaving only the coefficients and the constants in the last column.

    Entering The Coefficient Matrix Into The TI-89

    Step 1

    Press "On."

    Step 2

    Press "APPS" button. Press "6" for the "Data/Matrix Editor." Press "3" for "New." Press "->" for "Type:". Press "2" for "Matrix." Under "Variable," type "Coefficient." Press the "Enter" button. Under "Row Dimension," press "3." Under "Col Dimension," press "3." Press the "Enter" button twice.

    Step 3

    Fill in the empty 3 x 3 matrix with the coefficients from the equations. Once finished, press "2nd" button, then the "Exit" button.

    Entering The Constant Matrix Into The TI-89

    Step 1

    Press "APPS" button. Press "6" button for the "Data/Matrix Editor." Press "3" for "New." Press "->" for "Type:". Press "2" for "Matrix." Under "Variable," type "Constant." Press the "Enter" button. Under "Row Dimension," press "3." Under "Col Dimension," press "1." Press the "Enter" button twice.

    Step 2

    Fill in the empty 3 x 1 matrix with the column of constants from the equations (the number on the right side of the "=" sign in each equation).

    Step 3

    Once finished, press "2nd" and then the "Exit" button.

    Solving The Equations

    Step 1

    Press "2nd." Press "5" and then "4" and then "5." The word "SIMULT(" should appear on the lower right side of the screen.

    Step 2

    Press "2nd."Press the "-" button ("Var-Links" will be written in yellow above the button). Scroll down to "Coefficient" and press "Enter." Press "," button. Press "2nd." Press "-" button for Var-Link. Scroll down to "Constant" and press "Enter." Press ")" and then "Enter."

    Step 3

    Translate the resulting 3 x 1 matrix in the final solution: the top number equals x, the middle number equals y and the bottom number equals z.

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    About the Author

    A Chicago-based copywriter, Andy Pasquesi has extensive experience writing for automotive (BMW, MINI Cooper, Harley-Davidson), financial services (Ivy Funds, William Blair, T. Rowe Price, CME Group), healthcare (Abbott) and consumer goods (Sony, Motorola, Knoll) clients. He holds a Bachelor of Arts in English from Harvard University but does not care for the Oxford comma.

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