Gaussian Elimination

  • Interchange two equations
  • Multiply an equation by a non-zero constant
  • Add a multiple of one equation to another

    Systematic Method

  • Save the x term in equation 1 and use it to eliminate all the other x terms below it via rk' = c r1 + rk
  • Ignore equation 1 and use the y term in equation 2 to eliminate all the y terms below it.
  • Continue until the matrix is in echelon form
  • The last non-zero equation will yield xk=b, and then back substitution can be used.