Section 16.1: Systems of Linear Equations

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16.1 Outline

  1. Terminology
    1. system of equations
    2. simultaneous solution
    3. linear system
  2. Graphing method
    1. inconsistent system
    2. dependent system
  3. Substitution method
    1. equivalent systems
    2. procedure
  4. Linear combination (addition) method
    1. terminology
    2. procedure

 

16.1 Essential Ideas

To solve a system of equations means to find all replacements of the variables that make all of the equations true at the same time.

The graphing method consists of graphing each equation on the same coordinate system and then looking for the point or points of intersection.

The substitution method consists of the following steps:

  1. Solve one of the equations for one of the variables.
  2. Substitute the expression that you obtain into the other equation.
  3. Solve the resulting equation.
  4. Substitute that solution into either of the original equations to find the value
    of the other variable.
  5. State the solution.

The addition method consists of the following steps:

  1. Multiply one or both of the equations by a constant or constants so that the coefficients of one of the variables become opposites.
  2. Add corresponding members of the equations to obtain a new equation in a single variable.
  3. Solve the derived equation for that variable.
  4. Substitute the value of the found variable into either of the original equations, and solve for the second variable.
  5. State the solution.