Unit 2 Equations and Systems Review

Ross is picking out a pumpkin to buy at the local pumpkin farm. Each pumpkin costs $7.00 plus $0.45 per pound. Which equation represents the price of a pumpkin, p, that is x pounds?

• 0.45x + p = 7

• 0.45p + x = 7

• 7 + 0.45x = p

• 7x + 0.45 = p

On a trip to visit her friend, Anita has already walked 1 mile. She is currently walking at an average speed of 2 miles per hour.

Graph the function that shows the number of hours, h, the rest of the trip will take and the total number of miles, m, that Anita will walk. 

John walks at a constant speed.  The distance in miles, m, John walks is equal to m = p × h, where p is his pace in miles per hour at which he walks and h is the amount of time in hours he walks for.

What is an equation that can be used to find the pace, p, at which John walks.

• p = h/m

• p = m/h

• p = h*m

Sam claims that the solution to  12x + 2(2x - 10)  is  92 . She wants to prove this claim using the four assumptions below. Sam shows the following steps to prove her claim that the solution to the equation is x = 7.

12x + 2(2x - 10) = 92

Match  the number of the assumption used in each step of the proof.

• Assumption 3Addition Property of Equalit

• Step 3: 16x = 112

• Assumption 1: Combining Like Terms

• Step 4: x = 7

• Assumption 4 Division Property of Equali

• Step 2: 16x - 20 = 92

• Assumption 2: Distributive Property 

• Step 1: 12x + 4x - 20 = 92

​

A linear equation is given below:

3/4(2x + 8) = 4.5x

Drag and drop the correct steps into the boxes to show how to solve the equation.

(Hint: Do not make your first step distribution.)

Step 1: ​ (a)  

Step 2: ​ (b)  

Step 3: ​ (c)  

​

• 2x + 8 = 6x
• 4x = 8
• x = 2
• x + 4 = 6x - 3/4
• 2x + 8 = 3.375x
• 8x = 8
• 1.375x = 8
• x = 1
• x = 5.8

What is the solution to the following equation?

3(x + 2) + 0.5(4x + 6) = 34

Mathematical Equivalence

ON

​

Plot three points from each equation :

3x + 2y = 4

3x − 2y = −4

Then identify the solution​ on the graph.

Mike needs to solve the following system of equation using the elimination method.

6x + 10y = 54

3x - 3y = 3

He decides to use the elimination method to cancel out the x terms in order to first solve for y.  Mike uses the following steps:

Step 1:

6x + 10y = 54

-2(3x-3y) = -2(3)  

Step 2:

6x + 10 y = 54

-6x + 6y = -6

Step 3:

16y = 48

Step 4: 

y = 3

Did Mike use the correct steps to solve for y?

• Yes, Mike solved for y correctly.

• No, Mike should have only multiplied the -2 with the left side in step 1

• No, Mike should have multiplied the entire equation by positive 2 in step 1.

• No, Mike should have subtracted 16 in the last step instead of dividing it.

​

The school store sells pens for $0.75 each and pencils for $0.25 each. Anthony spent $6.25 to buy a total of 11 pens and pencils.

How many pens did Anthony buy? 

​

Noah is buying a pair of jeans and using a coupon for 25% off. The total price is $86.50, which includes $2.75 in sales tax. Noah's purchase can be modeled by the equation:

x – 0.25x + 2.75 = 86.50

A. What does the solution to this problem mean in this situation? ​ (a)  

B. Which represents a coefficient? ​ (b)  

C. Which answer represents a term in the equation? ​ (c)  

​

• Cost of the jeans before the coupon.
• -0.25
• Cost of the jeans after the coupon.
• Total cost of the jeans with tax.
• 0.25
• 2.75
• 86.50