HELP TOPIC: Solving Simultaneous Equations with the TI 89 & 92 Calculators

Example 1 – 2 EQ, 2 UK

x + 2y = 1 EQ1

3x + 4y = -1 EQ2

Solution Method 1 – "Solve"

- Press F3 (Solve)
- Select (down arrow to) 4:Solve( and ,{x,y}) [* see note 1]
- Press ENTER
- Edit the command line to read as follows:

Solve(x+2y=1 and 3x+4y=-1,{x,y})

- Press ENTER
- The display will report the solution as:

x = -3 and y = 2

* note 1: TI 89 (and likely the TI 92 PLUS). The procedure is more involved on the older TI 92:

On the TI 92 press F2 Algebra & select 1:solve( then ENTER. solve( will appear on the command line. Continue typing, adding to the command line so that it looks like this (without the quotes): "solve(x+2*y=1,y)". After entering the display will show your command line entry and its solution (rewritten here on one line): y = -(x-1)/2 . Repeat the procedure to solve the second equation so the new command line looks like this (without the quotes): "solve(3*x+4*y=-1,y)". After entering the display will show your command line entry and its solution (rewritten here on one line): y = -(3*x+1))/4. Next type the following on a new command line (without the quotes): "solve(-(x-1)/2=-(3*x+1)/4,x)". After entering the display will show your command line entry and its solution: x=-3 . Finally type the following on a new command line (without the quotes): "solve(x+2*y=1|x=-3,y)". After entering the display will show your command line entry and its solution: y=2 . You could also have typed on the last new command line (without the quotes): "solve(3*x+4*y=-1|x=-3,y)". This will also produce the solution y=2 . One final note: you can save typing time by moving the 4-way joy button to select items from the display to paste into your command line at the cursor. Remember also that pressing F2 Algebra & selecting 1:solve( then ENTER will place "solve(" (without the quotes) on a new command line.

Solution Method 2 – "Simult"

- Press 2
^{nd}alpha (locks in alpha entry mode) - Type "simult" and press alpha (unlocks alpha entry mode). (NOTE: The letter "T" is a black key in the same row as the X, Y, and Z black keys). On the TI 89 you can get "simult(" (without the quotes) to appear on the (new) command line by pressing: "2nd", "5 key", "Down joy botton"...to..."4:Matrix", "Right joy button", "Down joy botton"...to..."5:simult(", "ENTER". The button sequence is exactly the same for the older TI 92. The TI 92 PLUS may likely have the same button sequence to access "simult(".
- Continue typing: ([[1,2][3,4]],[[1][-1]]) and ENTER
- The display will show a "stacked" version of the command line of the following form:

simult([coefficients matrix],[column vector of constants])

and to the right side of the display
[column vector of the solution]. For this problem the solution
vector (written here as a row vector) is [-3 2]. We interpret
this as x = -3 and y = 2 .

Example 2 – 3 EQ, 3 UK

25x – 20y – 0z = 10 EQ1

-20x + 45y – 15z = -15 EQ2

-0x - 15y + 40z = -7 EQ3

Solution Method - "simult" (NOTE: Must use this for more

than 2 UK on all three TI models discussed here)

- Press 2
^{nd}alpha (locks in alpha entry mode) - Type "simult" and press alpha (unlocks alpha entry mode). (NOTE: The letter "T" is a black key in the same row as the X, Y, and Z black keys). See step 2 directly above for the button sequence to place "simult(" on the (new) command line.
- Continue typing: ([[25,-20,0][-20,45,-15][0,-15,40]],[[10][-15][-7]]) and ENTER

The display will show a "stacked" version of the command line of the following form:

simult([coefficients matrix],[column vector of constants])

and to the right side of the display
[column vector of the solution]. For this problem the solution
vector (written here as a row vector) is [-6/85 -7/17
–28/85]. If we press the "green" key and then
ENTER we get the numerical result (written here as a row vector)
is [.070588 -.411765 -.329412]. We interpret this as x = .070588,
y = -.411765, and z = -.329412 .