1. As a team discuss the following questions, be prepared for anyone to be asked to respond for the team. Do NOT re-state definitions from the book, use your words to “explain” the meanings.
What is a “system of equations”?
What is a “solution for AN equation?”
What is a “solutions for a SYSTEM of equations”?
How does graphing equations allow us to “figure out” the solution for a system of equations?
How many solutions are their any given system of equations?
How do we solve systems using the graphing method?

2. As a team, Discuss how to solve each of the following, then solve for the indicated variable. (NO Graphing allowed!)
If 3x + 2y = 23 and y = 4; Solve for x
2. If 3x + 2y = 23 and x = 3; solve for y

3. 3x + 2y = 23 and
y = 2x + 1 solve for x
3x + 2y = 23
-2x + y = 1

4. Substitution Method for Solving Systems of Equations
Lesson 7.2: Solving Systems using Substitution
Substitution Method for Solving Systems of Equations
Solve one of the equations for one variable
Substitute the resulting expression from step 1 into the OTHER original equation and solve for remaining variable.
Substitute the value from step 2 into one of the ORIGINAL equations to solve for the other variable.
CHECK your solution by !!

5. Examples: Solve using substitution
3x + y = 5
2x – y = 10
2x – y = 10
2x – (5 – 3x) = 10
2x + -1(5 + -3x) = 10
2x x = 10
5x + -5 = 10
5x =
5x = 15
3x + y = 5
3x + y – 3x = 5 – 3x
y = 5 – 3x
3x + y = 5
3(3) + y = 5
9 + y = 5
9 + y - 9 = 5 - 9
y = -4
x = 3
Solution: (3, -4)
Check Solution in each equation.

6. 3x + y = 5
2x – y = 10
Check Solution (3, -4)
3x + y = 5
3(3) + (-4) = 5
= 5
5 = 5
2x – y = 10
2(3) – (-4) = 10
6 + 4 = 10
10 = 10

7. 2) x + 2y = 4
-x + y = 7
-x + y = 7
-x + y = 7
-x + y + x = 7+x
y = x + 7
x + 2y = 4
x + 2(x+ 7) = 4
x + 2x + 14 = 4
3x + 14 = 4
3x + 14 – 14 = 4 – 14
3x = -10
Solution :

8. x = 2y
2x + 6y = 15
2x + 9 = 15
2x + 9 – 9 =
2x = 6
2(2y) + 6y = 15
4y + 6y = 15
10y = 15
Solution:

9. Homework: p , #20-40 mult. of 4
# 42, , 44, 45