Algebra 1 Notes Lesson 7-2 Substitution

Mathematics Standards -Patterns, Functions and Algebra: Solve real- world 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 4(4y) – y = 75 4x – y = 75

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75 16y – y = 75 15y = y = 5

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75 16y – y = 75 15y = y = 5

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75 16y – y = 75 15y = 75 x = 4y y = 5

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75 16y – y = 75 15y = 75 x = 4y = 4(5) y = 5

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75 16y – y = 75 15y = 75 x = 4y = 4(5) x = 20 y = 5

Example 1 Use substitution to solve the system of equations. x = 4y 4(4y) – y = 75 4x – y = 75 16y – y = 75 15y = 75 x = 4y = 4(5) x = 20 (20, 5) 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 y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 – x y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 8 x + y = -2 – x y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 82x + 2(-2 – x) = 8 x + y = -2 – x y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 82x + 2(-2 – x) = 8 x + y = -2 – x y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 82x + 2(-2 – x) = 8 x + y = -2 2x – 4 – 2x = 8 – x y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 82x + 2(-2 – x) = 8 x + y = -2 2x – 4 – 2x = 8 – x y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 82x + 2(-2 – x) = 8 x + y = -2 2x – 4 – 2x = 8 – x – x -4 = 8 y = -2 – x

Example 2 Use substitution to solve the system of equations. 2x + 2y = 82x + 2(-2 – x) = 8 x + y = -2 2x – 4 – 2x = 8 – x – x -4 = 8 y = -2 – x No Solution

Homework Pgs – 28 (evens) 50 – 53 (all)