Algebra 1 Notes Lesson 7 2 Substitution Mathematics
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 = 4 y 4 x – y = 75
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75 16 y – y = 75 15 15 y=5
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75 16 y – y = 75 15 15 y=5
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75 16 y – y = 75 15 y = 75 x = 4 y 15 15 y=5
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75 16 y – y = 75 15 y = 75 x = 4 y = 4(5) 15 15 y=5
Example 1 Use substitution to solve the system of equations. x = 4 y 4 x – y = 75 4(4 y) – y = 75 16 y – y = 75 15 y = 75 x = 4 y = 4(5) x = 20 15 15 y=5
Example 1 Use substitution to solve the system of equations. x = 4 y 4(4 y) – y = 75 4 x – y = 75 16 y – y = 75 15 y = 75 x = 4 y = 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) 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x 2 x + 2(-2 – x) = 8
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x 2 x + 2(-2 – x) = 8
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x 2 x + 2(-2 – x) = 8 2 x – 4 – 2 x = 8
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x 2 x + 2(-2 – x) = 8 2 x – 4 – 2 x = 8
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x 2 x + 2(-2 – x) = 8 2 x – 4 – 2 x = 8 -4 = 8
Example 2 Use substitution to solve the system of equations. 2 x + 2 y = 8 x + y = -2 –x –x y = -2 – x 2 x + 2(-2 – x) = 8 2 x – 4 – 2 x = 8 -4 = 8 No Solution
Homework Pgs. 379 12 – 28 (evens) 50 – 53 (all)
- Slides: 25