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 = 75

15 15

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

15 15

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 15 15

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) 15 15

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) 15 15

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) 15 15

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 – 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 2x + 2(-2 – x) = 8

x + y = -2

– x – x

y = -2 – x

Example 2

Use substitution to solve the system of equations.

2x + 2y = 8 2x + 2(-2 – x) = 8

x + y = -2

– x – x

y = -2 – x

Example 2

Use substitution to solve the system of equations.

2x + 2y = 8 2x + 2(-2 – x) = 8

x + y = -2 2x – 4 – 2x = 8

– x – x

y = -2 – x

Example 2

Use substitution to solve the system of equations.

2x + 2y = 8 2x + 2(-2 – x) = 8

x + y = -2 2x – 4 – 2x = 8

– x – x

y = -2 – x

Example 2

Use substitution to solve the system of equations.

2x + 2y = 8 2x + 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 = 8 2x + 2(-2 – x) = 8

x + y = -2 2x – 4 – 2x = 8

– x – x -4 = 8

y = -2 – x No Solution

Homework

Pgs. 379

12 – 28 (evens)

50 – 53 (all)