Solutions: Systems of 3 variable Equations

No Solution of three variable systems

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.
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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.
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One Solution of three variable systems

If the three planes intersect as pictured below then the three variable system has 1 point in common, and a single solution represented by the black point below.
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Infinite Solutions of three variable systems

If the three planes intersect as pictured below then the three variable system has a line of intersection and therefore an infinite number of solutions.
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