Questions

zMath Intervention Math (19-36) - Unit 33: Systems of Equations

Some of the questions in this unit may be answered by recording an audio file. If you chose to record the answer, click on the "Add Recording" button and follow the on-screen instructions closely. Once you have completed and attached the recording, enter the word “COMPLETE” in the text box. (Note: If your computer does not have a built-in microphone, a microphone or microphone/headset combination is needed to record audio.) Slope-Intercept Form

1) Identify the slope and y-intercept of the line with the given equation.

a.) slope = 2, y-intercept = (0, –3/4)

b.) slope = –3/4, y-intercept = (0, 2)

c.) slope = 2, y-intercept = (0, 3/4)

d.) slope = –3/4, y-intercept = (2, 0)

Print out or copy the given coordinate plane. Graph the line for the given equation. Apply the slope-intercept method of graphing. Point A is already graphed and is part of the line graph of the equation. Refer to the graph to answer the next four questions. Click to view the coordinate plane in a pop-up window.

2) Point A is the:

a.) vertical change (rise)

b.) horizontal change (run)

c.) x-intercept

d.) y-intercept

e.) slope

3) The fraction 2/3 is the:

a.) vertical change (rise

b.) horizontal change (run)

c.) x-intercept

d.) y-intercept

e.) slope

4) How is the slope applied to find a second point on the line?

a.) Count 3 units up and 2 units to the right and draw a point.

b.) Count 3 units up and 2 units to the left and draw a point.

c.) Count 2 units up and 3 units to the right and draw a point.

d.) Count 2 units up and 3 units to the left and draw a point.

5) What are the coordinates that represent a second point on the line of the given equation?

a.) (–2, 4)

b.) (3, –3)

c.) (3, 3)

d.) (2, 4)

6) Which procedure is the process of converting the equation, 3x – 4y = 12, from standard form to slope-intercept form?

a.) Procedure A

b.) Procedure B

c.) Procedure C

d.) Procedure D

7) Express the equation, 3x – 2y = 6 in slope-intercept form by solving for “y”.

a.) y = (3/2)x + 3

b.) x = (2/3)y + 2

c.) x = (2/3)y – 2

d.) y = (3/2)x – 3

8) What is the equation for the given graphed line?

a.) y = –3x + 5

b.) y = 3x + 5

c.) y = –3x – 5

d.) y = 3x – 5

9) Match the given equations with their correct graphs. Which statement is true?

a.) Graph A matches the equation y = (–2/3)x – 3.

b.) Graph B matches the equation y = (3/2)x – 3.

c.) Graph C matches the equation y = (2/3)x – 3.

d.) Graph D matches the equation y = (–2/3)x – 3.

10) Express the equation 2x + 4y = 8 in slope-intercept form by solving for y, and then graph the equation. Which equation and graph represent the equation 2x + 4y = 8? State the letter of the correct answer.

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11) Study Kelly’s solution, and then explain what she did incorrectly in solving the following problem: State the slope and y-intercept for the given equation, and then graph the equation.

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12) Alicia bought a $35 bus pass. Each time she rides the bus, $1.75 is deducted from the pass. The linear equation y = –1.75r + 35 represents the amount of money on the bus pass after "r" rides. Identify the slope and y-intercept of the line of the equation.

a.) m = –1.75; y-intercept = (0, 35)

b.) m = 35; y-intercept = (0, –1.75)

c.) m = 1.75; y-intercept = (0, –35)

d.) m = –35; y-intercept = (0, 1.75)

13) Referring to the previous problem, suppose Alicia rode the bus 10 times. How much money will be left on the pass?

a.) $19.25

b.) $17.50

c.) $15.75

d.) $14

14) Which statement is true about the solutions of the system of equations represented in each of the three given graphs?

a.) Graph A shows one solution. Graph B shows an infinite number of solutions. Graph C shows no solutions.

b.) Graph A shows an infinite number of solutions. Graph B shows one solution. Graph C shows no solutions.

c.) Graph A shows no solution. Graph B shows an infinite number of solutions. Graph C shows one solution.

d.) Graph A shows one solution. Graph B shows no solutions. Graph C shows an infinite number of solutions.

15) The graph of a system of two equations is shown below. What is the solution of the system of equations? Each space on the grid represents one unit.

a.) (–3, –2) or x = –3, y = –2

b.) (3, 2) or x = 3, y = 2

c.) (–3, 2) or x = –3, y = 2

d.) (2, –3) or x = 2, y = –3

For the next three problems, graph the system of equations to decide if there is one solution, many solutions, or no solutions. Follow the steps below. Step 1: Solve each equation for “y” (slope-intercept form).

Step 2: Plot the y-intercept and use the slope ratio (m) of rise/run to plot more points.

Step 3: After graphing both equations, determine how many solutions the system of equations has.

16) The given system of equations has how many solutions?

a.) The system of equations has one solution.

b.) The system of equations has no solution.

c.) The system of equations has many solutions.

17) The given system of equations has how many solutions?

a.) The system of equations has one solution.

b.) The system of equations has no solution.

c.) The system of equations has many solutions.

18) The given system of equations has how many solutions?

a.) The system of equations has one solution.

b.) The system of equations has no solution.

c.) The system of equations has many solutions.

For the next three problems, graph the system of equations to determine the solution. Follow the steps below. Step 1: Solve each equation for “y” (slope-intercept form).

Step 2: Plot the y-intercept and use the slope ratio (m) of rise/run to plot more points.

Step 3: After graphing both equations, determine the point of intersection (x, y).

19) What is the solution to the system of equations?

a.) There is no solution.

b.) (–3, –2)

c.) There are many solutions.

d.) (–2, –3)

20) What is the solution to the system of equations?

a.) (–3, 2)

b.) There is no solution.

c.) (–2, 3)

d.) There are many solutions.

21) What is the solution to the system of equations?

a.) There is no solution.

b.) (0, –4)

c.) There are many solutions.

d.) (4, 0)

22) Solve the system of equations by using substitution.

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23) Solve the system of equations by using substitution.

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24) Solve the system of equations by using substitution.

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25) Solve the system of equations by using substitution.

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26) A satellite company offers two plans for high-speed internet service shown below. Using substitution, solve the system of equations below. In how many months will the total cost of the two plans be equal?

a.) x = 12 months

b.) x = 15 months

c.) x = 18 months

d.) x = 21 months

Refer to the following scenario to solve the next two problems. After graduating from college, Dave is offered two engineering jobs. The table summarizes the pay offered for each job. After several years, the total pay accumulated will be the same. Click to view the chart in a pop-up window.

27) Solve the system of equations located in the table. In how many years will the salary be equal for both jobs and what will the salary equal that year. (Note: The graph was created with a graphing calculator.)

a.) x = 10 years, y = $65,000

b.) x = 9 years, y = $62,500

c.) x = 12 years, y = $69,000

d.) x = 15 years, y = $77,500

28) If Dave plans to stay at this job for over 15 years, which job should he choose?

a.) Engineering Company A

b.) Engineering Company B

29) The Celsius temperatures and Fahrenheit temperatures can be compared by graphing each formula as an equation as shown below. Solve the systems of equations below to determine when the temperatures are the same in both the Celsius and Fahrenheit scales.

a.) x = –32, y = –32

b.) x = 0, y = 0

c.) x = –25, y = –25

d.) x = –40, y = –40

Applications of Systems of Equations

30) The Lady Blue Devils scored 23 more points than the Lady Red Devils. The total of the two teams’ scores was 87. How many points did each team score? Fill in the partially completed equations to create a system of equations, and then solve. Consider the steps provided below to set up equations for the problem.

Let B stand for number of points scored by Blue Devils.

Let R stand for number of points scored by Red Devils.

The Lady Blue Devils scored 23 more points than the Lady Red Devils.
B = R ? 23

The total of the two teams’ scores was 87.
B ? R = 87

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Globes and maps of the earth usually show grid lines. These lines are called latitude lines and longitude lines. Earth is shaped like a sphere that makes the gridlines circles or parts of circles. Circles may be divided in degrees. Therefore, measures of latitude and longitude are expressed in degrees. On the map, point Z is located at 0 degrees latitude (the equator) and 0 degrees longitude (the prime meridian). The line that runs horizontally through the point is the 0 degrees latitude line and the line that runs vertically through the point is the 0 degrees longitude line.

All other points are either located right or left of 0 degrees longitude (the prime meridian) or above and below 0 degrees latitude (the equator).

For example: Point Q is located 120 degrees W and 20 degrees S. Point A is located 100 degrees E and 60 degrees N.

Click to view the map in a pop-up window.

31) What is the latitude and longitude of the place in North America marked with point N?

a.) 40 degrees S, 80 degrees E

b.) 40 degrees N, 80 degrees W

c.) 40 degrees S, 80 degrees W

d.) 40 degrees N, 80 degrees E

32) Which ocean could have a latitude of 20 degrees south and a longitude of 60 degrees east?

a.) Pacific Ocean

b.) Atlantic Ocean

c.) Indian Ocean

d.) Oceania

33) Estimate the latitude and longitude of your home to the nearest 5 degrees. Name the nearest large city in your country.

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