CCGPS Coordinate Algebra

EOCT ReviewUnits 1 and 2

Unit 1: Relationships Among Quantities

Key Ideas

Expressions, Equations & Inequalities

• Arithmetic expressions are comprised of numbers and operation signs.

• Algebraic expressions contain one or more variables.

• The parts of expressions that are separated by addition or subtraction signs are called terms.

• The numerical factor is called the coefficient.

Example 5: 4x2 +7xy – 3

• It has three terms: 4x2, 7xy, and 3. • For 4x2, the coefficient is 4 and the

variable factor is x. • For 7xy, the coefficient is 7 and the

variable factors are x and y. • The third term, 3, has no variables

and is called a constant.

Example 6:The Jones family has twice as many tomato plants as pepper plants. If there are 21 plants in their garden, how many plants are pepper plants?• How should we approach the solution

to this equation?

tomato plant: 2x

pepper plant: x 2x x 21 x 7

Example 7:Find 2 consecutive integers whose sum is 225.

first: x

second: x + 1x x 1 225

x 112

112&113

Example 8:A rectangle is 7 cm longer than it is wide. Its perimeter is at least 58 cm. What are the smallest possible dimensions for the rectangle?

4x 14 58

x 11

11 by 16

Writing Linear & Exponential Equations

• If the numbers are going up or down by a constant amount, the equation is a linear equation and should be written in the form y = mx + b.

• If the numbers are going up or down by a common multiplier (doubling, tripling, etc.), the equation is an exponential equation and should be written in the form y = a(b)x.

Create the equation of the line for each of the following tables.

9) 10) x y0 21 62 183 54

x y0 -51 32 113 19

xy 2(3) y 8x 5

11. Linear Word ProblemEnzo is celebrating his birthday and his mom gave him $50 to take his friends out to celebrate. He decided he was going to buy appetizers and desserts for everyone. It cost 5 dollars per dessert and 10 dollars per appetizer. Enzo is wondering what kind of combinations he can buy for his friends.

a) Write an equation using 2 variables to represent Enzo’s purchasing decision. (Let a = number of appetizers and d = number of desserts.)

b) Use your equation to figure out how many desserts Enzo can get if he buys 4 appetizers.

c) How many appetizers can Enzo buy if he buys 6 desserts?

5a 10d 50

5 4 10d 50 d 3

5a 10 6 50 a 2

12. Exponential Word Problem:

Ryan bought a car for $20,000 that depreciates at 12% per year. His car is 6 years old. How much is it worth now?

ty P 1 r

6y 20,000 1 .12

y $9,288.08

Solving Exponential Equations

• If the bases are the same, you can just set the exponents equal to each other and solve the resulting linear equation.

• If the bases are not the same, you must make them the same by changing one or both of the bases.– Distribute the exponent to the given

exponent.– Then, set the exponents equal to each other

and solve.

Solve the exponential equation:

13) 14) 2 23 27x x4 8 72 2x x

4x 8 x 7

x 5

3 x 22x3 3

2x 3 x 2

x 6

Unit 2: Solving Systems of Equations

Key Ideas

Reasoning with Equations & Inequalities

• Understanding how to solve equations

• Solve equations and inequalities in one variable

• Solve systems of equations• Represent and solve equations and

inequalities graphically.

Important Tips

• Know the properties of operations

• Be familiar with the properties of equality and inequality. (Watch out for the negative multiplier.)

• Eliminate denominators (multiply by denominators to eliminate them)

Properties to know• Addition Property of Equality• Subtraction Property of Equality• Multiplication Property of Equality• Division Property of Equality• Reflexive Property of Equality• Symmetric Property of Equality• Transitive Property of Equality• Commutative Property of Addition and

Multiplication• Associative Property of Addition and Multiplication• Distributive Property• Identity Property of Addition and Multiplication• Multiplicative Property of Zero• Additive and Multiplicative Inverses

Example 15

Solve the equation 8(x + 2) = 2(y + 4) for y.

y 4x 4

Example 16Karla wants to save up for a prom dress.

She figures she can save $9 each week from the money she earns babysitting.

If she plans to spend up to $150 for the dress, how many weeks will it take her to save enough money?

17weeks

Example 17

• This equation can be used to find h, the number of hours it takes Bill and Bob to clean their rooms.

• How many hours will it take them?

15 20

h h 4h h 20

h 4

Example 18• You are selling tickets for a basketball

game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450.

• Use a system of linear equations to determine how many student tickets you sold?Student: x

General:y

x y 350

3x 5y 1450

150 student

Example 19You sold 52 boxes of candy for a fundraiser. The large size box sold for $3.50 each and the small size box sold for $1.75 each. If you raised $112.00, how many boxes of each size did you sell?

A. 40 large, 12 smallB. 12 large, 40 smallC. 28 large, 24 smallD. 24 large, 28 small

large : x

small:y

x y 52

3.5x 1.75y 112

Example 20You sold 61 orders of frozen pizza for a fundraiser. The large size sold for $12 each and the small size sold for $9 each. If you raised $660.00, how many of each size did you sell?

A. 24 large, 37 smallB. 27 large, 34 smallC. 34 large, 27 smallD. 37 large, 24 small

large : x

small:y

x y 61

12x 9y 660

Example 21

Which equation corresponds to the graph shown?A. y = x + 1B. y = 2x + 1C. y = x – 2D. y = -3x – 2

Example 22Which graph would represent a system of linear equations that has no common coordinate pairs?

A B

C D

Ex. 23 Graph

2

2

y x

x