My calculator will only show one line/ t-table at a time... I cannot "turn on" both y1 & y2

m, the slope of a straight line is also called the rate of change of the function. Its definition is m=(y2-y1)/(x2-x1) where (x1,y1) are the coordinates of one point on the line, and (x2,y2) are the coordinates of a second point on the lines.

This is problem with graphing differential equation. Invalid Axes error occurs if Axes=TIME or if t(time) is set as a CUSTOM axis. This is important to noticed: if Fields=DIRFLD you cannot plot a time axis. See captured image:




This graph represented differential system of equations y1'(x)=y2(x), y2'(x)=-y1(x) for initial conditions y1(0)=0, y2(0)=-1.Finally, x axes=y1(x) and y axes=y2(x)

The site seems to eat the plus signs I enter, so I will use PLUS to symbolize addition.

To find the equation of the straight line (y = a*x PLUS b) that passes through two points P1(x1,y1) and P(x2,y2) , you need to use
1. the coordinates of the points to calculate the slope a (gradient) as a=(y2-y1)/(x2-x1)
2. Replace the calculated value of a in the equation and write that one of the points ( P1(x1,y1) for example) satisfies the equation. In other words y1=a*x1 PLUS b.
Here y1 and x1 are known values, a has been calculated, and only b is still unknown. You can now use the equation y1=a*x1 PLUS b to calculate b as
b=(y1-a*x1)

Example: Equation of the line through (1,5) and (3,6)
Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=6, y1=5, x2=3, and x1=1. You should get a=(6-5)/(3-1)=1/2
The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=(1/2)*3 PLUS b.
Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5
Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

I trust you can substitute you own values for (x1,y1, x2,y2) to duplicate the calculations above.

Example: Equation of the line through (1,5) and (3,6)
Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=6, y1=5, x2=3, and x1=1. You should get a=(6-5)/(3-1)=1/2
The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=3/2 PLUS b.
Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5
Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=1, y1=0, x2=0, and x1=-6. You should get a=(1-0)/(0-(-6))=1/6
The y-intercept is the y-cordinate for x=0. Its value is 1.
The equation is then y=(x/6) 1.

1.) make sure the two lines are not the same line

2.) under the y= button, when you enter the two equations make sure for both y1 and y2 the icon on the far left for both is a solid \ and the = on the right of y1 and y2 should be highlighted.

3.) clear memory if all else fails as a last resort.

hope this helps

Let us see if I understand what you want to do. You have two functions f and g. With f and g you create four functions,

1. f+g, which you want to evaluate at 0
2. f-g, which you want to evaluate at -1
3. f*g, which you want to evaluate at 1
4. and f/g, which you want to evaluate at 3

If that is not what you intend to do, then I am sorry to I that interpreted incorrectly and you will have to post a comment with more information.
If however I did understand what you want to do, then there is a simple way to achieve this

1. In the [Y=] function editor, enter Y1 and Y2
2. In your mind decide which one represents f(x) and which represents g(x), probably f(x)=Y1(x) and g(x)= Y2(x)
   
3. Validate each one by pressing [ENTER]
   
4. Do not worry about graphing the function.
5. Press [2nd][QUIT] to return to main calculator screen
6. Enter a value (for example 5) and store it in variable X; to do so you press 5 [STO->][X,T, theta,n] [ENTER]
7. To calculate f(x)+g(x) or (f+g)(x) on the command line in main calculator screen

• Press [VARS][=>][Y-VARS][1:Function][1:Y1][ENTER]. Main calculator screen echoes Y1
• Press [+]. Screen shows Y1+
  
• Press [VARS][=>][Y-VARS][1:Function][1:Y2][ENTER]. Main calculator screen echoes Y1+Y2
• Press [ENTER] to obtain the value of f+g at X=5
  

As you can see, if you want a different operation f-g, f*g, or f`/g for a different value of X, you will have to repeat steps 6 and 7.

I am going to show you how to create a small program that will perform all the 4 operations in sequence, each time asking you for the value of X you want to use. If you are not interested, you can ignore what follows. I remain convinced that it will be helpful for other visitors.

Creating a simple program

Press [PRGM]
Use arrow to highlight [NEW]
Press [ENTER]
Screen displays
PROGRAM
Name= with alpha cursor blinking
Type in the name, for example FOPG ( meaning F operation G) or anything else. Do not use a keyword (reserved command of the TI84Plus) These are what you find in the [CATALOG].



The top line on each screen capture is inserted by the program editor after you choose the name. The last line of first screen is the the same line as the second line on 2nd screen. It must not be entered. The colon : is supplied by the program editor. It is the beginning of an instruction.

There are only to commands that are repeated here: Disp and Prompt

Disp orders the program to display

1. a message (what is between the quotation marks) or
   
2. the result of a calculation: Y1+Y2, Y1-Y2, Y1*Y2, or Y1/Y2

Prompt X will display X=? and the blinking cursor. You are supposed to enter the desired value of X and press [ENTER].
The Disp and Prompt command are accessed through the command catalog by pressing [2nd][0] (CATALOG) then scrolling along the list of commands to find the one needed. Shortcuts are possible (see below)

How to key in the program steps within the program editor
: Disp "F+G"

Press [2nd][0] (CATALOG) [X^-1](D) [Scroll Down [till...] Disp
Press [ENTER]. Editor shows :Disp
Press [ALPHA] [+] ("). Editor shows :Disp "
Press [ALPHA][COS] (F). Editor shows :Disp "F
Press [+]. Editor shows :Disp "F+
Press [ALPHA][TAN] (G). Editor shows :Disp "F+G
Press [ALPHA][+] (") Editor shows :Disp "F+G"
Press [ENTER] to validate instruction
Calculator inserts a new line :

: Disp Y1+Y2
Press [2nd][0] (CATALOG) [X^-1](D) [Scroll Down [till...] Disp
Press [ENTER]. Editor shows :Disp
Press [VARS][=>][Y-VARS][1:Function][1:Y1][ENTER]. Editor shows :Disp Y1
Press [+] . Editor shows :Disp Y1+
Press [VARS][=>][Y-VARS][1:Function][1:Y2][ENTER]. Editor shows :Disp Y1+Y2
Press {ENTER] to validate instruction
Editor inserts a new line :


:Prompt X
Press [2nd][0] (CATALOG) [8](P) [Scroll Down [till...] Prompt
Press [ENTER]. Editor shows :Prompt
Press [X,T.theta,n] key. Editor shows :Prompt X
Press [ENTER] to validate instruction
Editor inserts a new line :

To save program
Once all instructions are entered, press [2nd][QUIT] to save program.

To run program

1. Press [PRGM]
2. Under the [EXEC] menu, the list of available programs appears.
3. Type the number corresponding to the one you want to run ( FOPG) and press [ENTER].
4. The main calculator screen displays prgmFOPG and blinking cursor.
5. Press [ENTER] to make it run
6. Enter a value of X and press [ENTER]
7. Follow instructions.

Hi,
In the Y= equation editor you can enter two functions, and graph them both or calculate a table for both. However, the two functions will be evaluated at the same values of X.

Rather than trying to guess what is happening, I will show you how to get your two tables.

If you have used one the applications Inequalz or Transform it si probably still stuck in memory, and you must unload it from the RAM before recovering the usual calculator behavio(u)r

1. Press the [APPS] button, find Inequalz or Transform, point to it and click [ENTER].
2. You will be asked to Continue or Quit the application.
3. Press the number corresponding to Quit (usually 2).
4. Press [2nd][Y=] (STAT PLOT). Press [4:PlotsOff][ENTER]
   
5. Calculator replies Done.

Open the [Y=] equation editor. Type in your equations. Press [ENTER] at the end of each equation. Verify that the [=] signs after Y1, and Y2 remain highlighted when cursor is moved away from them.
Press [2nd][GRAPH] (Table) to see your 2 tables y1 and y2 calculated at the same X.

Hope it helps.
Thank you for rating the solution.

Hello,
Here how you do it taking as exemples y1=x^3 -5 and y2=abs(x^3-5)
Turn calculator ON by pressing [AC/On] . Use arrows to select [Graph] icon and press [EXE]
On line Y1= enter X[^]3 -5 [EXE]
On line Y2= press [OPTN] [F5:NUM][F1:abs] [(] X [^]3 -5 [)] [EXE]
The graphs will be drawn one after the other. You might have to adjust the window limits.
Here is an ouput drawn on another calculator.

For negative values of the x-variable, Y1 has negative values, while in the same range, Y2 has positive values, equal and opposite to those of Y1. In that range, Y1 and Y2 are symetric of each other with respect to the X axis.
For positive values of the x-variable, Y1 and Y2 are identical.

Hope it helps

I have had the same problem luckily i figured out what to do. 1. press the apps button 2. then there should be an unwanted app(it was the only one on mine) 3. pick it and hit enter 4. go to uninstall on the top of ur screen problem solved!!!! hope this helped