What can we expect

This activity considers sets of equations having three unknowns. In this case, we know that the solutions of a single equation form a plane. If it helps with visualization, consider using $3\times5$-inch index cards to represent planes.

1. Is it possible that there are no solutions to two linear equations in three unknowns? Either sketch an example or state a reason why it can't happen.

2. Is it possible that ther…

1. Which of the following equations are linear? Please provide a justification for your response.

   1. .

   2. .

   3. .

2. Consider the system of linear equations:

   1. Is $(x,y,z) = (1,2,0)$ a solution?

   2. Is $(x,y,z) = (-2,1,0)$ a solution?

   3. Is $(x,y,z) = (0,-3,1)$ a solution?

   4. Can you find a solution in which $y = 0$?

   5. Do you think there are other solutions? Please explain your response.