Question

# First, create 3 equations of the form class="katex">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.

use calculator calculator website GeoGebra

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 $x=g(y,z)=0y+0z=0$ . 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.

*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.

*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.

*x*=0

*y*=0

*z*=0

*x*= 0 can be seen as the constant function $x=g(y,z)=0y+0z=0$ . Use GeoGebra to "observe" the system.

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