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)