First, create 3 equations of the form ax+by+cz=d, where a, b, c, and d are constants (integers between - 5 and 5). For example, x+2y-z=-1. Perform row operations on your system to obtain a row-echelon form and the solution.

1. Reflect on what the graphs are suggesting for one equation, two equations, and three equations, and describe your observations. Think about the equation as a function f of x and y, for example, x+2y+1=z in the example above. Geogebra automatically interprets this way, that is, like z=f(x, y)=x+2y+1, it isolates z in the equation.

2. What did the graphs show when you entered the second equation?

3. Give a simple description of the system

x=0

y=0

z=0

x = 0 can be seen as the constant function x=g(y, z)=0y+0z=0. Of course, you can use GeoGebra to "observe" the system.

4. Give an example with 2 equations as simple as possible with 3 variables (at least 1 being non-linear; keeping z to the one power on both equations) and describe the potential of GeoGebra to study nonlinear systems.