How to solve two linear equation in three variables using Casio fx-82MS? x+y+z=100 5x+y+0.05z=100

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

Sorry, It is not possible to solve equations on the Casio FX-82 ms. Try the Casio FX-115 ES/ FX-115 ES Plus, FX-991ES/ FX-881 ES Plus C.

There is no equation solving mode (utility) on this calculator. Sorry.

There is no equation solving utility on this calculator. Sorry.

Sorry, the Fx-115W is unable to solve equations of any type. In addition to that, the more sophisticated Casios such as the FX-991 ES solve linear equations of no more than 3 variables.

Thhe Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.
The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Alternatively, after you create the system of 4 linear equations you can use the matrix utility to find Real(x), Im(x), Real(y) and Im(y) and recompose the x and y.

The Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.
The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Do you really need a calculator to solve a linear equation?
Let us see how to solve it without a calculator.
Remove the parentheses fronm the second term on the left : y-3
Use the distributive property on the last term on the right side -2y-6
Take the term -3 to the right side, changing its sign in the process (becomes +3)
Take the -2y term to the left making it +2y.
3y +2y=18+3-6 or 5y=15 and the answer is straightforward .

As to your Casio FX300ES, it cannot solve equations because it does not have an EQUATION calculation mode. The Casios FX-115ES and FX-991ES have an Equation Mode. If you use any of the two to solve an equation in one variable (linear, quadratic or other) the unknown is taken to be x by default. You would have to change the name of the variable from y to x.

Press key Mode, first select option 5:EQN (by pressing key 5), then option 2: a_nX+b_nY+c_nZ=d_n (by pressin 2).
Now input coefficients from equations in table (each column is for one variable), just type in number and press =, then use arrows to move to another cell.

This calculator cannot handle matrices that have anyone dimension larger than 3.
How to solve your problem?

1. Set up the problem by hand (pencil paper): use Cramer's rules. Make use of the calculator to perform the various calculation.

OR

1. Sacrifice one equation which you will use to eliminate one variable of the 4 by expressing it in terms of the other three. Do the algebra to obtain a system of 3 equations in three unknowns.
2. Use the calculator to find the solutions ( the three variables that are left).
3. Use the 4th equation (the one you scacrificed) to obtain the value of the 4th unknown.
   

OR

use a computer program devoted to solving linear equations

OR buy another calculator that can handle larger systems of equations (a graphing calculator, maybe).