1. Solving Real World Linear Systems of Equations with Two Variables Objective: Review writing and solving linear systems of equations with two variables. By: Ariel Eller

2. Submit Menu Learn how to use this activity Click the picture of the question mark if you need help. Click the picture of the house to go home. Click the arrow on the left to go back one page. Click the arrow on the right to go forward one page. Click the Submit button to submit your answer.

3. Submit  What you should know:  How to solve linear systems of equations with 2 variables  You may need to use Distance= rate*time  Writing and solving inequalities Review This review gives you an opportunity to work at your own pace and review at home if you would like.

4. If you need to review substitution watch this video. Be sure to enable content to watch the video and try using Firefox web browser.

5. If you need to review addition watch this video. Be sure to enable content to watch the video and try using Firefox web browser.

6. Submit The information will be presented here. Example Problem: The question will be presented here. In the text box to the right type you answer. Then click submit to check your answer. The answer will appear here when you click submit.

7. Submit First, let us practice writing a system of equations in a real world application. Problem 1: A 400 space parking garage includes 180 regular spaces, with the rest of the spaces being compact car spaces. The garage will only let regular cars park in regular spaces, but compact cars may park in any type of space. Write a system of inequalities that represents this situation. First, what do we know from the information we are given. Type your answer in the text box below. We know that: There are 400 total parking spaces 180 of them are regular parking spaces

8. Submit First, let us practice writing a system of equations in a real world application. Problem 1: A 400 space parking garage includes 180 regular spaces, with the rest of the spaces being compact car spaces. The garage will only let regular cars park in regular spaces, but compact cars may park in any type of space. Write a system of equations inequality that represents this situation. Now, label the unknown variables in the text box below, such as x and y (describe to me what x and y are in the problem). x= number of regular cars y= number of compact cars

9. Submit First, let us practice writing a system of equations in a real world application. Problem 1: A 400 space parking garage includes 180 regular spaces, with the rest of the spaces being compact car spaces. The garage will only let regular cars park in regular spaces, but compact cars may park in any type of space. Write a system of equations inequality that represents this situation. Finally, now that we know what x and y are we can write two inequalities with our information. Type your answer in the text box below. x≤180 x+y≤400

10. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hour. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? First, identify what questions you are being asked. Type your response in the test box below. We want to know: The speed of the motorboat and the speed of the current.

11. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Now that we know what variables we are looking for, let us assign labels to the unknowns. Place your answer in the text box below. x=speed of the motor boat y=rate (speed) of the current

12. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Now identify what information you know. Place your answer in the text box below. Dawn travels 21 miles each direction. Dawn travels 2 hours upstream. Dawn travels 1 hour downstream.

13. Remember we know distance = rate * timed=r*t  Use (x-y) to show rate as the boat travels upstream (against the current).  Use (x+y) to show rate as the boat travels down stream (with the current).

14. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Let’s write the first equation for the boat moving upstream. Follow the format d=r*t Place your answer in the text box below. 21=(x-y)*2

15. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Now write the second equation for the boat moving downstream. Use the format d=r*t. Place your answer in the text box below. 21=(x+y)*1

16. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Now that we have our two equations we need to rewrite them. For the first equation multiply both sides by ½. (1/2)*21=(x-y)*2*(1/2) Similarly, multiply the second equation by 1 on both sides. 1*21=(x+y)*1*1

17. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Use the information from the last page to write your final equations. Place your answer in the text box below. 21/2=x-y 21=x+y

18. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? Now we can use the addition method to solve for the speed of the boat, x, and the speed of the current, y. Place your answer in the text box below. 21/2=x-y + 21 =x+y 63/2=2x What does x equal? x=15.75 or 63/4 mph

19. Submit With her motor boat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1 hours. Problem 2: How fast could her motorboat go in still water? What is the rate of the current? If x=15.75 mile per hour, now we can substitute this value in for x in the second equation 21=x+y. What does y equal? Place your answer in the text box below. x=5.25 mph

20. Practice Problems Click on an image to practice each story problem.

21. Submit At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Practice Problem 1: Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind? Place your answer in the text box below. x=451 mph Click here if you got it wrong

22. Submit A company uses two vans to transport workers from a free parking lot to the workplace between 7:00am and 9:00am. One van has 5 more seats than the other. The smaller van makes two trips every morning while the larger one makes only one trip. The two vans can transport 65 people maximum. Practice Problem 2: Let x be the seats in the small van and y the seats in the large van. How many seats does the larger van have? Place your answer in the text box below. y=25 seats in the larger van Click here if you got it wrong

23. Submit A mail distribution center processes as many as 150,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier takes 1800 pieces per load and each air carrier 1500 pieces per load. The loading equipment is able to handle as many as 150 loads per day. Practice Problem 3: Let x be the number of loads by land carriers and y the number of loads by air carriers. Write a system of inequalities represents this situation? Place your answer in the text box below. 1800x+1500y≤150,000 x+y≤150 Click here if you it wrong

24. Submit Maple Grove wants to include two types of maple trees, the namesake of the city, for their parks. Two varieties of maple trees have been selected. One variety costs $80 per tree; the other more colorful variety costs $85 per tree. The tree budget must not exceed $75,000. Citizens want more of the colorful $85 trees than the others if possible. Practice Problem 4: Let x be the number of $80 trees and y the number of $85 trees. Write a system of inequalities to represent this situation. Place your answer in the text box below. $80x+$85y≤$75,000 y≥x or x≤y Click here if you got wrong

25. Submit  Set up your equations 2460=(x-y)*6 2460=(x+y)*5  Simplify your equations by multiplying by 1/6 and 1/5 410=x-y 492=x+y Solve using the addition method. 410=x-y +492=x+y 902=2x x=451mph y=41mph

26. Submit  Set up your equations y=x+5 2x+y=65  Solve using the substitution method. 2x+(x+5)=65 3x+5=65 3x=60 x=20 Solve for y by substituting x back into the first equation, y=x+5. y=20+5

27. Submit  Set up your equations  Remember if something cannot exceed a number this means less than or equal to ≤  If something must exceed a number this means greater than ≥ Now write your equations: 1800x+1500y≤150,000 x+y≤150

28. Submit  Set up your equations  Remember if something cannot exceed a number this means less than or equal to ≤  If something must exceed a number this means greater than ≥ Now write your equations: 80x+85y≤75,000 y≥x or x≤y