Systems of Equations

A system of equations is a set of equations of more than 1 variable. In a system of equations, we want to find the values of the variable which will satisfy each of the equations. We typically divide these types of systems into two types, linear and nonlinear

Linear Systems

Linear Systems are systems in which all equations can be expressed in terms of addition and subtraction of multiples of a fwe unknown variables.

The following are examples of linear systems

• example 1
  • 3 x + 2 y = 4
  • 2 x - 6 y = 5
• exmaple 2
  • 3 x = 4 (trivial...but linear)
• exmaple 3
  • 3 x + 2 y = 4
  • 2 x - 6 y + 5 z = 5
  • 2 x - 6 y - z = 5

Nonlinear Systems

Nonlinear systems of equations are characterized by having terms which cannot be formed by simply adding together multiples of the unknown variables. Possibly unknowns are exponetiated, multiplied together, or are the arguments of a function.

The following are examples of nonlinear systems

• example 1
  • 3 xy + 2 y = 4 (x * y is not linear)
  • 2 x - 6 y = 5
• exmaple 2
  • 3 x² = 4 (x * x is not linear)
• exmaple 3
  • 3 x + 2 y = 4
  • 2 x - 6 y + 5 z = 5
  • 2 x - 6 y - sin(z) = 5 (sin(z) is not linear)