Solve Linear Systems by Adding Section 6 3

Solve Linear Systems by Adding Section 6. 3 beginning on page 386

The Elimination Method The elimination method involves adding the equations together in order to eliminate one of the variables. In order to eliminate a variable you need opposite terms. (I get very excited when opposites are already in the equations and all of the like terms are lined up!) - Add the equations - Solve for the remaining variable - Substitute the found value into one of the original equations to find the value of the second variable. - Write your solution as a coordinate pair. 2

Arranging Like Terms -Rewrite the second equation so that the like terms (and the equal sign) are lined up. (subtract 3 x from both sides) - Follow the same steps we did in the previous example.

Word Problem For a floral arrangement class, Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects. She has to pay for the twigs and flowers that she uses in her arrangement. Each twig costs $1 and each flower costs $3. Alicia spends $15 on twigs and flowers. Write and solve a system to find the number of twigs and the number of flowers she used. One equation will represent the number of objects she uses, and the other will represent how much money she is spending. Declare your variables. x = The number of twigs, y = The number of flowers **** Instead of adding the equations, we can also subtract them. We do this when we have the same exact terms rather than opposite terms. ***

Elimination Method - Subtracting To subtract you must change the sign of each term in the equation you are subtracting. Alicia used 6 twigs and 3 flowers.

Practice Answers: 1) (-1, -3) 4) (1, 1) 2) (2, -3) 3) (5, 4) 5) (-2, 0) 6) (1, 2)