What is a linear equation with 3 variables?
The picture on the left is the graph of the plane 2x + 3y + z = 6.
The red triangle is the portion of the plane when x, y, and z values are all positive. This plane actually continues off in the negative direction. All that is pictured is the part of the plane that is intersected by the positive axes (the negative axes have dashed lines).
What is a system of 3 variables equations?
on Systems of 3 variable equations
No Solutions, 1 Solution or Infinite Solutions
Like systems of linear equations, the solution of a system of planes can be no solution, one solution or infinite solutions.
Below is a picture of three planes that have no solution. There is no single point at which all three planes intersect, therefore this system has no solution.
The other common example of systems of three variables equations that have no solution is pictured below. In the case below, each plane intersects the other two planes. However, there is no single point at which all three planes meet. Therefore, the system of 3 variable equations below has no solution.