1. Mrs. Meehan 6th Grade Algebra

2. Combining unlike terms
I can simplify algebraic expressions

3. Do Now: Simplify each expression =
= 6

4. term
3X³Y
coefficient variables
Like terms are terms that contain the same variables raised to the same exponent.
X and 3X
2Y² and -5Y²
3X²Y and ½X²Y
6 and 8
2X² and 2X
r³ and t³
3rt³ and -0.5rt³
Are Unlike Terms
Are Like Terms
Are Like Terms

5. Look at these 10 terms. Find all the like terms that can be combined:

6. Construct a like term that could combine with each of these terms.
7a³b²
¾mn³ 4

7. Combine Like Terms Example 1
7x² - 4x²
= (7-4) x²
= 3x²
Notice that we can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

8. Practice Simplify each expression by combing like terms.
12x + 30x
= 42x
6.8y² - y²
= 5.8y²
-4n + 11n²
-4n and 11n² are not like terms. Do not combine them
-20t – 8.5t
= -28.5t 1

9. Simplify the following expression by combining like terms:
6xy + 3x²y + xy + 6x²y + 10xy +
6xy
3x²y
1xy
6x²y
10xy
17xy
9x²y

10. Distributive Propertyn n n n n n 1 1 1 1 1 1 1 1 1 1 1 1
3(n+2) n + 6
3(n + 2) n + 6

11. Distributive Property
What is the Distributive Property?
How to use the Distributive Property in simplifying algebraic expressions?
Watch video Distributive Property Basics

12. Example 2 Simplify 2(x+6) + 3x. Try this:
1) 6(x - 4) ) -12x - 5x + 3a + x
Procedure
Justification
1. 2(x+6)+3x
2. 2(x)+2(6)+3x
Distributive Property
3. 2x x
Multiply
4. 2x + 3x + 12
Commutative Property
5. 5x + 12
Combine like terms

13. Solving equations
I can solve equations

14. What is a solution of an equation?
What is an equation?
What is a solution of an equation?
How do we find the solutions of an equation?
Answer

15. An equation is like a balance scale.
What are the rules for keeping an equation balanced?
What ever you do to
One side of the equal
Sign must be done to
The other side too
Use opposite math to isolate the variable on one side of the equal sign

16. Motivation

17. 2 bags + 4 blocks = 3 bags + 2 blocks
How many are in one ?
2 bags + 4 blocks = 3 bags + 2 blocks
- 2 bags bags
4 blocks = 1 bag + 2 blocks
- 2 blocks blocks
2 blocks = 1 bag

18. Check ?
and = and
Since = =
8 blocks blocks

19. Example 1 Solve 3x – 8 = 7. Check your answer. +8 +8 3x = 15 3 3 x = 5
3x = 15
x = 5
Check 3x – 8 = 7
3(5) – 8 7
15 – 8 7
7 7

20. Example 2
Solve 4(x – 2) + 2x = 40
4x – 8 + 2x = Distributive Property
6x – 8 = combine like terms
add 8 on both sides of the
equation
6x = 48
divide 6 on both sides of
the equation
x = 8

21. Solving Algebraic Equations
1.Use the distributive property to get rid of any parenthesis
2.Combine like terms
3.Move all of the variables to one side of the equal sign (make sure it is positive!)
4.Get the variable by itself by doing opposite math to both sides of the equal sign
5.Check your answer by substituting it into the original equation

22. Practice -4 + 7x = 3 2a + 3 – 8a = 8 9 = 6 – (x + 2)
Click here, if you need help.

23. I can solve systems of linear equation in two variables by elimination

24. Do Now:
A farmer has ducks and cows. There are 8 heads and 22 feet. How many ducks and cows does he have?

25. Guess and Check a has __ feet ; a has __ feet2 4
The # of Ducks
The # of Cows
Total # of Heads
Total # of Feet 1 2
6=1*2+2*2 4 12 3 6 18 8 24 7 20 5 22

26. Method one: Use one variable to set up an equation.
Let x = the amount of ducks, then 8-x = the amount of cows
the # of ducks’ feet * the # of ducks + the # of cows’ feet * the # of cows =total # of feet
2 * x * ( 8 – x ) = 22
2x + 32 – 4x = 22
-2x + 32 = 22
-2x = -10
x = 5
the amount of cows = 8 – x = 8 – 5 = 3
So, there are 5 ducks and 3 cows.

27. The Idea of Elimination 6 + - + -

28. Development Example 1 elimination using addition
Solve x – 2y = by elimination
5x + 2y = 1
Step 1 Add (1) and (2) to eliminate the y-terms.
6x = -18
Step 2 Simplify and solve for x.
x = -3
Step 3 Write one of the original equations.
x – 2y = -19
Step 4 Substitute -3 for x.
-3 – 2y = -19
Step 5 Simplify and solve for y
-2y = -16
y = 8
(1)
(2)

29. Development Example 2 elimination using subtraction
Solve x + 4y = by elimination
-2x + 4y = 8
Step 1 Subtract (1) and (2) to eliminate the y-terms.
5x = 10
Step 2 Simplify and solve for x.
x = 2
Step 3 Write one of the original equations.
3x + 4y = 18
Step 4 Substitute 2 for x.
3(2) + 4y = 18
Step 5 Simplify and solve for y
6 + 4y = 18
4y = 12
y = 3
(1)
(2)

30. Go Back to the Do Now Let d = the # of ducks and c = the # of cows
In some case, we will first need to multiply one or both of the equations by a number so that one variable has opposite coefficients. This will be the new step 1.
(1) * 2  2(d+c) = 8*2
2d + 2c = 16 (3)
(2) – (3)  2c = 6 c = 3 cows
Substitute c=3 into (1) or (2), but (1) would be easier
d + c = 8  d + 3 = 8  d = 5 ducks
Therefore, the farmer has 3 cows and 5 ducks.