SOLVING SYSTEMS OF LINEAR EQUATIONS BY ELIMINATION Section 17.3

Using the Elimination Method The elimination method utilizes the addition property of equality: For example or Still adding the same thing to both sides since C = D.

Using the Elimination Method Consider the system A = B C = D A+C=B+D

Using the Elimination Method Consider the system Uh oh. Cannot solve an equation in two variables. Adding worked because one variable had opposite coefficients and thus added to zero and was eliminated.

Using the Elimination Method For elimination to work, one of the variables must have opposite coefficients.  If not, you can use the multiplication property to change the coefficients. This method is also called linear combination, or addition.

Using the Elimination Method Consider the system  Solve using addition by eliminating either variable.  Multiply the equations by any value that will produce opposite coefficients on either variable. Must multiply one entire equation by the same value, but can use a different value for the other equation. -3( ) ( )-3 Substitute to get x = 3 -2( ) ( )-2 Substitute to get y = -4 OR