How to Solve for Simultaneous Equations With an HP 48
The HP 48g solves simultaneous equations by converting them to a system of linear equations and then performing matrix calculations on them. Linear equations are related equations consisting of the same variables; 2-variabled equations appear in rows as "ax+by=c" forms, where "a" and "b" are coefficients, "x" and "y" are variables, and "c" is a constant. Matrices are sets of numbers, made up of rows and columns. The form lends itself well to matrix form since each equation makes a row and each coefficient makes a column.
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Instructions
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1
Rewrite the equations in "ax+by=c" form. For example, you begin with the two equations
2x-2y-3=0 and 8y=7x+2
Transforming them into "ax+by=c" form would result in
2x-2y=3 and 7x-8y=-2.
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2
Press the "Solve" key. Then press the downward-facing white arrow key in the upper right-hand area of the keypad and select the "Solve Linear System" selection. Press the "Enter" key. This will open the "solve system A * X= B" form. 3 rows labeled "A", "B", and "X" will appear on the screen.
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3
Enter the x- and y-coefficients into the first row of the "A" field in matrix form. The HP 48g signifies matrices by using separating statements for rows and columns. Using the example, type "[", then "[" again, then input "2", then "-2", and then "]". Then type "[" and enter "7" first, then "-8", and then "]" and "]" again. The screen should look as follows
A: [ [ 2 -2] [7 -8] ]
which represents the matrix
| 2 -2 |
| 7 -8 |.
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4
Move the cursor down to the "B" field using the white arrow keys. Key in the constants as a two rows of a matrix. Type "[" then type "[" again, then type "3", and then type "]". Then type "[", then type "-2", then type "]" and then "]" again. The input should appear on the screen as
B: [ [3] ] [ [-2] ], representing the matrix
| 3 |
|-2 |.
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5
Press the downward white arrow key to move the cursor to the row labeled "X." Press the "Solve" key. The answers will appear in the calculator's matrix form. For the example, the answers will be displayed as
X: [ [ 14 ] [ 12.5] ]
where x=14 and y=12.5.
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