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Algebra

Solve a system of three equations

Find x, y and z for three linked equations.

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The example is x + y + z = 6, 2x − y + z = 3 and x + 2y − z = 2. The answer is x = 1, y = 2, z = 3. Check: 1 + 2 + 3 = 6, 2 − 2 + 3 = 3 and 1 + 4 − 3 = 2.

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Open MENU, go to Equation/Func (press up three times, then =), choose 1 for Simul Equation and 3 for three unknowns.

    MENU▲▲▲=13

  2. Type each row as the numbers in front of x, y, z and the right side. Press = after each: 1 1 1 6, then 2 −1 1 3, then 1 2 −1 2.

    1=1=1=6=2=(−)1=1=3=1=2=(−)1=2=

You should seex=1 y=2 z=3

Natural Scientific 991 key reference · Natural Scientific 991 manual

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Press MENU, 5 for Equation, F1 for Simultaneous, then F2 for 3 unknowns.

    MENU5F1F2

  2. Fill the grid with EXE after each number, row by row.

    1EXE1EXE1EXE6EXE2EXE(−)1EXE1EXE3EXE1EXE2EXE(−)1EXE2EXE

  3. Press F1 (SOLVE).

    F1

You should seeX=1 Y=2 Z=3

Natural Color Graphing key reference · Natural Color Graphing manual

Classic Graphing 84 · Using rref on a matrix

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Open the MATRIX menu (2nd, x⁻¹), go right to MATH and choose rref( (letter B).

    2ndMATRIXx⁻¹▶alphaBapps

  2. Type the 3 by 4 table of numbers, row by row, with 2nd [ and 2nd ] around each row. Close the bracket and press enter.

    2nd[×2nd[×1,1,1,62nd]−2nd[×2,(−)1,1,32nd]−2nd[×1,2,(−)1,22nd]−2nd]−)enter

You should see[[1 0 0 1] [0 1 0 2] [0 0 1 3]]

The right-hand column holds x, y and z.

Classic Graphing 84 key reference · Classic Graphing 84 manual

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Press menu, 3, 1 for solve(. Type the three equations in curly brackets, then the unknowns {x, y, z} in curly brackets.

    menu31shift{(x+y+z=6,2x−y+z=3,x+2y−z=2shift}),shift{(x,y,zshift}))

  2. Press enter.

    enter

You should seex=1 and y=2 and z=3

Classic CAS key reference · Classic CAS manual

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