How to graph linear equation in two variables

First you must use a graphing calculator.
Most graphing calculators graph functions, i.e. relations of the form y=f(x).
Some graphing calculators are able to graph equations (not necessarily functions). On one of these calculators your draw the vertical line x=-3, then you shade to the left of the point x=-3. That gives you the real line from infinity up to but not including x=-3.
Generally, people do not need calculators to find the solutions to inequalities in just one variable.

You can type in an x-variable by pressing the x-var key.
For other graph types, the variables r, theta, t, can be enter by pressing the appropriate function key. from the graph equation entry screen.

Do you mean three (3) linear equations in 3 unknowns, or tree allometric equations? Thank you Al Gore for inventing the Internet.
For the second case, we really need to know the form of the functions in view of their graphical representation:
Since this calculator cannot do graphs, you can generate a table of values and then represent the variation on graphing paper (linear or logarithmique) depending on the form of the dependence.
Here is a link to the user's manual for this calculator.

Casio fx 4500P silrun Systems

You have attempted to use, edit, or delete an archived variable. For example, the expression dim(L1) produces an error if L1 is archived

After you enter the data draw the SCATTER plot first.
When you perform the (linear) regression analysis LineReg, save the regression equation to a function, for example Y1
The syntax is
LineReg L1, L2, Y1 ENTER


From the Stat>CALC menu press LineReg
The command echoes on command line
Press [2nd][1] to enter the L1 list on command line
Press [,] to separate
Press [2nd] [2] to enter L2 on the command line
Press [,] the comma again
Press [VARS][>][Y-Vars][1~Function][1:Y1] [ENTER]
Press [GRAPH] to have the regression line equation drawn
on the same screen as the Scatter Plot you drew before.

Strange. The calculator comes with a Getting Started manual. In any event you can download an electronic copy from education.ti.com.
From the associated icon of the calculator, I surmise that you have TI Nspire without the CAS (Computer Algebra System). Unfortunately, this version of the Nspire cannot perform symbolic algebra. It will use the distributive property by itself if you feed it expressions without letter symbols. If you type in expressions with symbols, all symbols must have a value stored in them. The exception is instances where you are trying to solve an equation (or a systems of linear equations).

To enter powers of trigonometric functions you must enclose the functions in parentheses and then apply the exponent to the whole. For example X1t =(sin T)^3 , Y1t=(cos T)^3 will give you a shape similar to a rhombus with concave sides. The symbol ^syands for the operation of raising to a power. The key is the one with the caret symbol ^ , and it is wedged between the xsqure and EXIT keys (third row of keys).
As regards the cotangent, use the equivalent definition cot(X)=1/tan(X).

You might not see the scatter plot when you go to the graph because the boundaries are not set correctly. With the scatter plot turned on, go to "zoom" and then scroll down to "zoomStat" and hit enter. Try going to the graph again and see if the the scatter plot shows up. As for the the equation being slightly different than the examples, this is probably just the calculator rounding up the answers it gets. Good luck!

When you press [STAT] and right Arrow to highlight CALC you see two linear regression model [4:LinReg(ax+b)] and [8:LinReg(a +bx)]
If you select [4: ...] the command echoes on main calculator screen as LinReg(ax+b) and a blinking cursor
If you press [ENTER] you will get your equation, a, b, and r^2 if DiagnosticsOn command has been executed before. However you will not be able to see the line of best fit on top of the raw data scatter plot.

To save the equation of best fit in a function variable, ex Y1, you complete the command as follows
LinReg(ax+b) [VARS][=>][Y-VARS][1:Function][1:Y1]
The Y1 variable will appear on main calculator screen, and you have
LinReg(ax+b) Y1
Press [ENTER]
Screen display the equation, its parameter and its correlation coefficients (if so configured).
Press [GRAPH] to draw the line of best fit on top of the scatter plot.

Here are two screen captures to show you the equation and the line of best fit.


As you can see from the value of r^2, and the graph, a linear regression does not seem good.

Although the coefficient of correlation is well defined for a few regression models, you do not calculate it directly because your calculator does that for you.
I could just tell you that it is displayed along with the statistical results (equation of best fitting curve, ) but if you do not know how to do that you will just shoot my post. If you know how to do a linear regression, stop right here and ignore what follows.

For those interested: How to do a regression on the calculator
I am sorry but I will have to assume that you know how to enter the data through the [MENU][STAT].

1. After you finish entering all the data
2. Press [F1:Graph], select Gph1, Gph2, or Gph3.
   
3. Once the graph of the experimental data is drawn, you will have access to the diverse regression models.
   
4. Your choices are
   
5. [X:Linear]
   
6. [Med-Med],
   
7. [Quadratic :X^2]
   
8. [Cubic;X^3]
   
9. [Quartic: X^4].
10. Press [F6] to scroll right to access the others
11. [Logarithmic:LOG],
    
12. [Exponential :EXP],
    
13. [Power :Pwr] and
    
14. [Sinusoidal: Sin]
    

After you select a model and press [EXE], the screen displays the equation and its various coefficients, a correlation coefficient if it has meaning, etc.
On that same screen, you have a menu option [F6:Draw]. If you select it, the regression curve will be drawn on the same screen as your statistical graph. This allows you to judge if the fit is good. If it is not, you have the option to choose another model.
The other option [F5:Copy] allows you to save the regression equation in the Y1, Y2, etc. variables.