1. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems To solve a system by substitution, you solve one equation for one variable and then substitute this expression into the other equation. Use substitution to solve the system of equations. y = x – 1 x + y = 7

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

3. 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

4. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems For the elimination method, 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. Use elimination to solve the system of equations. 3x + 2y = 4 4x – 2y = –18

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

6. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Find the solution to the system. 3x + y = 1 2y + 6x = –18

7. 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

8. 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 4: Zoology Application Let x present the amount of beef mix in the mixture. Let y present the amount of bacon mix in the mixture.

9. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Example 4 Continued Write one equation based on the amount of dog food: Amount of beef mix plus amount of bacon mix equals xy 60. 60+ = Write another equation based on the amount of protein: Protein of beef mix plus protein of bacon mix equals 0.18x0.09y protein in mixture. 0.15(60) + =

10. 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? Let x represent the amount of the Sumatra beans in the blend. Check It Out! Example 4 Let y represent the amount of the Kona beans in the blend.

11. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Write one equation based on the amount of each bean: Amount of Sumatra beans plus amount of Kona beans equals xy 50. 50 + = Write another equation based on cost of the beans: Cost of Sumatra beans plus cost of Kona beans equals 5x5x 13y cost of beans. 10(50) += Check It Out! Example 4 Continued

12. Holt Algebra 2 3-2 Using Algebraic Methods to Solve Linear Systems Homework pg. 194 #’s 22, 33, 36, 37