Definitions For Solving Systems Of Linear Equations By Substitution Method

This is the general form of a system of two equations:
ax + by = h
cx + dy = k
  • A system is a set of equations with several variables. The system we will use has two equations with two variables in each equation.

  • The system is a linear system when both equations used in the system are linear.

  • The solution set is the set of numbers that satisfy both equations simultaneously.


    Since a linear system of two equations is associated with two lines on a graph of the solution, there are three possible answer for the simultaneous solution.

    1. The system intersects at a single point (one solution).

    2. The inconsistent system has parallel lines that do not intersect at any point (no solution).

    3. The dependent system occurs when the two linear equations used are the same lines thus having an infinite number of points in common (infinite number of solutions).

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