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Algebra

Solve a system of two equations

Find x and y when 2x + y = 5 and x − y = 1.

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A system is a set of equations that must all be true together. For 2x + y = 5 and x − y = 1, adding the two equations removes y: 3x = 6, so x = 2, and then y = 1.

Most calculators have a mode where you only type the numbers in front of x, y and the number on the right side.

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 2 for two unknowns.

    MENU▲▲▲=12

  2. Row 1 is 2x + y = 5, so type 2, 1, 5. Row 2 is x − y = 1, so type 1, −1, 1. Press = after each number.

    2=1=5=1=(−)1=1=

You should seex=2 y=1

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 F1 for 2 unknowns.

    MENU5F1F1

  2. Fill the grid row by row with EXE after each number: 2, 1, 5, then 1, −1, 1.

    2EXE1EXE5EXE1EXE(−)1EXE1EXE

  3. Press F1 (SOLVE).

    F1

You should seeX=2 Y=1

Natural Color Graphing key reference · Natural Color Graphing 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 two equations inside curly brackets (shift + the open-bracket key), separated by a comma.

    menu31shift{(2x+y=5,x−y=1shift})

  2. Add a comma, then the unknowns in curly brackets {x, y}, close the bracket and press enter.

    ,shift{(x,yshift}))enter

You should seex=2 and y=1

Classic CAS key reference · Classic CAS 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. Write the system as one table of numbers (an augmented matrix): [[2, 1, 5] [1, −1, 1]]. Open the MATRIX menu with 2nd and the x⁻¹ key, go right to MATH and pick rref( (letter B).

    2ndMATRIXx⁻¹▶alphaBapps

  2. Type the matrix with 2nd and the [ and ] keys, close the bracket and press enter.

    2nd[×2nd[×2,1,52nd]−2nd[×1,(−)1,12nd]−2nd]−)enter

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

The last column of the result holds the answers: x = 2 and y = 1.

Classic Graphing 84 key reference · Classic Graphing 84 manual

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