Solve systems of equations using ELIMINATION

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Presentation transcript:

Solve systems of equations using ELIMINATION

Eliminate means to get rid of, so we are going to eliminate one variable to solve for the other. STEPS: 1) Line up equations so like terms are on top of each other 2) Eliminate one term BY (+ OR -) 3) Combine like terms 4) Solve for the variable that is left 5) Substitute to solve for the other variable

Elimination Using ___________ and _____________ works best when the coefficient on like terms are the ___________________of one another. Like Terms Opposites 2x and 2x 3x and -3x, 4y and 4y -5y and 5y Addition Subtraction same or opposite

When the coefficients are the same and you want to eliminate them, you need to _____________. subtract When the coefficients are opposites and you want to eliminate them, you need to______ . add

Solve using elimination by ADDITION or SUBTRACTION. 3x – 2y = 13 x + 2y = 7 3x – 5y = 3 4x + 5y = 4

– 4x + 2y = 8 4x – 3y = – 10 x – y = 4 x + y = 2

Solve using elimination by ADDITION or SUBTRACTION. 5x – y = – 6 – x + y = 2 6) x – y = 14 x + y = 20

Solve using elimination by ADDITION or SUBTRACTION. 7) 2x + 9y = 25 4x + 9y = 23 8) 7x + 2y = 24 8x + 2y = 30

Solve using elimination by ADDITION or SUBTRACTION. 9) 2x + 5y = 0 x + 5y = -10 10) 7x + 8y = 20 7x – y = 29

End Day #1

HONORS

Sometimes you will not be given two equations that have LIKE TERMS or OPPOSITES already written. When this happens you can multiple one equation, or BOTH equations by a number to create like terms or opposites.

Solve using elimination by MULTIPLICATION. 11) 8x + 14y = 4 -6x – 7y = -10 12) -4x -15y = -17 -x + 5y = -13

Solve using elimination by MULTIPLICATION. 13) 4x – 2y = 20 -8x – 3y = 16 14) 5x – 3y = -28 4x + 6y = -14

Application 15) Sam spent $24.75 to buy a dozen flowers for his mother. The bouquet contained roses and daisies. (Roses cost $2.50; Daisies cost $1.75) How many of each type of flower did Sam buy?

Elimination Word Problems

1. The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of one senior citizen ticket and one student ticket?

2. Castel and Gabriella are selling pies for a school fundraiser 2. Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castel sold 6 apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of $94. What is the cost each of one apple pie and one lemon meringue pie?

3. The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 3 child tickets for a total of $69. The school took in $91 on the second day by selling 5 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?

4. Ming and Carlos are selling cookie dough for a school fundraiser 4. Ming and Carlos are selling cookie dough for a school fundraiser. Customers can buy packages of chocolate chip cookie dough and packages of gingerbread cookie dough. Ming sold 8 packages of chocolate chip cookie dough and 12 packages of gingerbread cookie dough for a total of $364. Carlos sold 1 package of chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $93. Find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.

5. Kayla's school is selling tickets to the annual dance competition 5. Kayla's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 5 child tickets for a total of $70. The school took in $216 on the second day by selling 12 senior citizen tickets and 12 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

6. Amanda and Jennifer are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Jennifer sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127. Find the cost each of one package of tulips bulbs and one bag of daffodil bulbs.

7. The local amusement park is a popular field trip destination 7. The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 16 vans and 8 buses with 752 students. High School B rented and filled 5 vans and 5 buses with 380 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?