Wetzel

Math 102

4.3 – Systems of Linear Equations:

Elimination Method (Addition Method)

Elimination Method:  ( 1 of 3 methods to solve a linear system )

            To Solve:  ( 2 equations with 2 variables )

                        1.)  Write all equations in standard form.   ax + by = c

                        2.)  Get opposite coefficients for the x or y variables by multiplying one or both of the equations by a constant.

                        3.)  Add the two equations together  (The variable with the opposite coefficients should cancel) and SOLVE for the remaining variable.

                        4.)  Substitute this value into one of the original equations and solve for the other variable.

                        5.)  Write the answer as an ordered pair.

            Examples:

            1.)                                                                     2.) 

            3.)                                                                     4.) 

·        Infinitely Many Solutions:   All variables cancel and the remaining equation is TRUE.

·        No Solution:   All variables cancel and the remaining equation is FALSE.