An example of three (linear) equations in two unknowns is
\begin{eqnarray*} x+2y&=&3 \\ 4x-5y&=&6 \\ -7x + 8y&=&9 \end{eqnarray*}
Each of these equations gives a line in the plane. Three equations gives three lines in the plane.
How can three lines arrange themselves in the plane?
You could have three different parallel lines. You could have two different parallel lines and a transversal. You could have two concurrent lines and a third line parallel. You could have three non-parallel lines that all meet at a single point. There are many different possibilities.