Algebra 1 Notes Lesson 7-2 Substitution Mathematics Standards - Patterns, Functions and Algebra: Solve realworld problems that can be modeled using linear, quadratic, exponential or square root functions. - Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. - Patterns, Functions and Algebra: Solve real world problems that can be modeled using systems of linear equations and inequalities. Vocabulary Substitution – Second method for solving systems of equations. (First method was graphing) Vocabulary Substitution 1. Solve one equation for one variable (BE SMART) 2. Substitute for that variable in the other equation. Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 16y – y = 75 15y = 75 15 15 y=5 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 16y – y = 75 15y = 75 15 15 y=5 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 16y – y = 75 15y = 75 x = 4y 15 15 y=5 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 16y – y = 75 15y = 75 x = 4y = 4(5) 15 15 y=5 Example 1 Use substitution to solve the system of equations. x = 4y 4x – y = 75 4(4y) – y = 75 16y – y = 75 15y = 75 x = 4y = 4(5) x = 20 15 15 y=5 Example 1 Use substitution to solve the system of equations. 4(4y) – y = 75 x = 4y 4x – y = 75 16y – y = 75 15y = 75 x = 4y = 4(5) x = 20 15 (20, 5) 15 y=5 Example 2 Use substitution to solve the system of equations.(Be smart – what to solve for) 2x + 2y = 8 x + y = -2 –x –x y = -2 – x Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x 2x + 2(-2 – x) = 8 Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x 2x + 2(-2 – x) = 8 Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x 2x + 2(-2 – x) = 8 2x – 4 – 2x = 8 Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x 2x + 2(-2 – x) = 8 2x – 4 – 2x = 8 Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x 2x + 2(-2 – x) = 8 2x – 4 – 2x = 8 -4 = 8 Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 –x –x y = -2 – x 2x + 2(-2 – x) = 8 2x – 4 – 2x = 8 -4 = 8 No Solution Homework Pgs. 379 12 – 28 (evens) 50 – 53 (all)