Math Systems of linear equations Graphical method

Graphical method

In the graphical method one imagines the linear equations as a linear function.



A system of linear equations can have different solutions, which can be found graphically as follows:
  • one solution: the straight lines intersect at one point
  • no solution: the straight lines are parallel to each other
  • infinitely many solution: the straight lines are identical


  1. Convert the equations appropriately.
  2. Draw the graphs of the equations into a coordinate system.
  3. Read off intersection.


Determine graphically the solution set of the system of linear equations:

  1. $4x=4y-8$
  2. $y-6=-x$
  1. Convert the equations appropriately

    $4x=4y-8$   $|:4$
    $x=y-2$   $|+2$

    $y-6=-x$   $|:+6$
  2. Draw the lines in a coordinate system


  3. Determine the intersection and specify the solution set

    One intersection: $I(2|4)$
    => There is one solution