1. Solving Systems of Equations By Substitution
A-REI.3; A-REI.5; A-REI.6; A-REI.7

2. Table of Contents Pg
Title
LI/SC Foldable
Substitution Method Notes

3. Learning Intention/Success Criteria
LI: We are learning how to solve a system of equations by substitution SC: I know how to -determine if a system of equations has many solutions -determine if a system of equations has no solutions -determine if a system of equations has one solution -solve systems of two linear equations algebraically using substitution method -solve equations for a variable

4. Example 1: Solve the system of equations using substitution method 3x + y = 2 y = 2x – 3
3x + 1(2x – 3) = 2
3x + 2x – 3 = 2
5x – 3 = 2
+ 3
+ 3
__________________
5x = 5
___ 5
___ 5
x = 1

5. x = 1 y = 2x – 3
y = 2(1) – 3
y = 2 – 3
y = – 1
Solution: (1, -1)

6. Example 2: Solve the system of equations using substitution method x – 2y = 3 x – 2y = -4
_______________
x = 2y + 3
x = 2y + 3 x – 2y = -4
1(2y + 3) – 2y = -4
2y + 3 – 2y = -4
0y + 3 = -4
3 = -4
No Solution

7. Example 3: Solve the system of equations using substitution method y = 2x + 1 2y = 4x + 2
2(2x + 1) = 4x + 2
4x + 2 = 4x + 2
- 2
- 2
___________________
4x = 4x
Many solutions