2. Warm-up 1. Solve the following system of equations by graphing: 3x – y = -3 y – 3x = -3 2. Determine the solution type from the following system of equations: 2x – 3y = 9 -3x + 2y = -6 3. Graph this system of inequalities -3x + y > 4 -2y – 5x ≥ 8

3. y=3x-3 y=3x+3 No Solution

4. Solution Type 2x – 3y = 9 -3y = -2x + 9 y = 2/3x – 3 m = 2/3 b = -3 -3x + 2y = -6 2y = 3x – 6 y = 3/2x – 3 m = 3/2 b = -3

5. y ≤-5/2x - 4 y > 3x+4

6. Solving Linear Systems Algebraically with Substitution Section 3-2 Pages 160-1-67

7. Objectives I can solve word problems with systems of equations and substitution

8. Substitution Method Goal 1. Isolate one variable in one equation 2. Substitute into the other equation(s) AWAYS pick the easiest equation to isolate.

9. Word Problems When solving a word problem, consider these suggestions 1. Identify what the variables are in the problem 2. Write equations that would represent the word problem, looking for key words Sum, difference, twice, product, half, etc…

10. Example 1 GEOMETRY: The length of a rectangle is 3 cm more than twice the width. If the perimeter is 84 cm, find the dimensions. Variables: Length (L) Width (W) Equations: L = 2W + 3 2L + 2W = P Now, solve by substitution

11. Example 2 Melissa has 57 coins in dimes and nickels. The total value of the coins is $4.60. How many coins of each kind does she have? Nickels (N) Dimes (D) Equations: N + D = 57 10D + 5N = 460 Now, solve by substitution

12. Example 3 At a recent movie, adult tickets were $4.50 and student tickets were $2.50. During opening night a total of 300 tickets were sold earning $1130. How many of each ticket type were sold? Adult Ticket (A) Student Ticket (S) Equations: A + S = 300 4.50A + 2.50S = 1130 Now, solve by substitution

13. Homework Substitution Worksheet