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Simultaneous Linear Equations of Two Variables

7.1 Simultaneous Linear Equations of Two Variables

Geometry of Simultaneous Linear Equations

  • Suppose you are asked to solve the simultaneous equations \begin{cases}x-y=2 \\2 x+3 y=10\end{cases}. In fact, each equation represents a line, if drawn on a 2-D coordinate plane.
  • Thus, solving the simultaneous equations is similar to finding the intersection point of two lines.
  • Consider solving two simultaneous equations for two unknowns. Interpreting geometrically, we want to find the intersection point(s) of two lines. There are three possible scenarios:
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