1. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems 3-2 Using Algebraic Methods to Solve Linear Systems Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Do Now Determine if the given ordered pair is an element of the solution set of 2x – y = 5 3y + x = 6 1. (3, 1) 2. (–1, 1) Solve each equation for y. 3. x + 3y = 2x + 4y – 4 4. 6x + 5 + y = 3y + 2x – 1.

3. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems TSW solve systems of equations by substitution. TSW solve systems of equations by elimination. Objectives

4. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems substitution elimination Vocabulary

5. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems The graph shows a system of linear equations. As you can see, without the use of technology, determining the solution from the graph is not easy. You can use the substitution method to find an exact solution. In substitution, you solve one equation for one variable and then substitute this expression into the other equation.

6. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use substitution to solve the system of equations. Example 1: Solving Linear Systems by Substitution y = x – 1 x + y = 7

7. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use substitution to solve the system of equations. Example 2: Solving Linear Systems by Substitution 2y + x = 4 3x – 4y = 7

8. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use substitution to solve the system of equations. y = 2x – 1 3x + 2y = 26 Example 3

9. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use substitution to solve the system of equations. 5x + 6y = –9 2x – 2 = –y Example 4

10. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems You can also solve systems of equations with the elimination method. With elimination, you get rid of one of the variables by adding or subtracting equations. You may have to multiply one or both equations by a number to create variable terms that can be eliminated. The elimination method is sometimes called the addition method or linear combination. Reading Math

11. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use elimination to solve the system of equations. Example 5: Solving Linear Systems by Elimination 3x + 2y = 4 4x – 2y = –18

12. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use elimination to solve the system of equations. Example 6: Solving Linear Systems by Elimination 3x + 5y = –16 2x + 3y = –9

13. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use elimination to solve the system of equations. 4x + 7y = –25 –12x –7y = 19 Example 7

14. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Use elimination to solve the system of equations. 5x – 3y = 42 8x + 5y = 28 Example 7.5

15. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems In Lesson 3–1, you learned that systems may have infinitely many or no solutions. When you try to solve these systems algebraically, the result will be an identity or a contradiction. An identity, such as 0 = 0, is always true and indicates infinitely many solutions. A contradiction, such as 1 = 3, is never true and indicates no solution. Remember!

16. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Classify the system and determine the number of solutions. Example 8: Solving Systems with Infinitely Many or No Solutions 3x + y = 1 2y + 6x = –18

17. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Classify the system and determine the number of solutions. 56x + 8y = –32 7x + y = –4 Example 9

18. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Classify the system and determine the number of solutions. 6x + 3y = –12 2x + y = –6 Example 10

19. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems A veterinarian needs 60 pounds of dog food that is 15% protein. He will combine a beef mix that is 18% protein with a bacon mix that is 9% protein. How many pounds of each does he need to make the 15% protein mixture? Example 11: Zoology Application

20. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems A coffee blend contains Sumatra beans which cost $5/lb, and Kona beans, which cost $13/lb. If the blend costs $10/lb, how much of each type of coffee is in 50 lb of the blend? Example 12

21. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems The Miller and Benson families went to a theme park. The Millers bought 6 adult and 15 children tickets for $423. The Bensons bought 5 adult and 9 children tickets for $293. Find the cost of each ticket. Example 13

22. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Lesson Quiz Use substitution or elimination to solve each system of equations. 3x + y = 1 y = x + 9 1. (–2, 7) 5x – 4y = 10 3x – 4y = –2 2. (6, 5) 3. The Miller and Benson families went to a theme park. The Millers bought 6 adult and 15 children tickets for $423. The Bensons bought 5 adult and 9 children tickets for $293. Find the cost of each ticket. adult: $28; children’s: $17