One Solution To A Set Of 3 Linear Equations With 3 Variables

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I am trying to understand the geometry of that solution set. If there is one solution thats mean that there is only one place where those 3, 3 Dimensions intersect, that mean that 2 of them are touching the other one, and each other with their corners?

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More like three planes oriented in different directions all touch each other at one point. The first two planes form a line of intersection, and the final plane intersects with that line at one point.