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| Graphing Systems of Equations |
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| In the following problems, graph each system of equations on graph paper, and then determine if the graph is correct, the classification of the system, and the correct solution if the given solution is incorrect. |
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1) Is the graph correct? What is the classification of the system? If the graph is not correct, give the correct solution.
Hint: Solve each equation for y and check the slopes and y-intercepts. If the slopes and y-intercepts do not check, then graph each line on paper to find the solution. |
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2) Is the graph correct? What is the classification of the system? If the graph is not correct, give the correct solution.
Hint: Solve each equation for y and check the slopes and y-intercepts. If the slopes and y-intercepts do not check, then graph each line on paper to find the solution. |
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3) Is the graph correct? What is the classification of the system? If the graph is not correct, give the correct solution.
Hint: Solve each equation for y and check the slopes and y-intercepts. If the slopes and y-intercepts do not check, then graph each line on paper to find the solution. |
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| 4) Describe the solution for a consistent, independent system of linear equations and give an example of a system of equations to justify your response. |
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| Substitution Method for Solving Systems of Equations
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| Use substitution to solve the system of equations in the following problems. |
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Elimination Method for Solving Systems of Equations
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| Use elimination to solve the system of equations in the following problems. If there is a solution, express the answer as an ordered pair; otherwise, indicate "No solution" or "Many solutions". |
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| Applications of Linear Systems |
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| 12) Two groups of students order tacos and burritos at a Mexican restaurant. The first group bought 3 tacos and 5 burritos and spent $11.52. The second group bought 7 tacos and 9 burritos and spent $22.64. Let t represent the price per taco and let b represent the price per burrito. Write and solve a system of equations to find the cost of one taco and the cost of one burrito. |
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| 13) For the previous problem, solve the system of equations and state the cost of one taco and one burrito. |
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14) An airplane flying into a head wind travels the 2400 miles flying distance between two cities in 6 hours. On the return flight, the same distance is traveled in 5 hours. Find the air speed of the plane and the speed of the wind, assuming that both remain constant. (The air speed is the speed of the plane if there were no wind.) Complete the chart and write a system of equations.
Hint: Model each equation after the formula, distance equals rate times time. (d = rt) |
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| 15) For the previous problem, solve the system of equations and state the speed of the airplane and the speed of the wind current. |
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| Graphing Linear Inequalities |
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For the following problems, graph each linear inequality on graph paper. Compare the solution to the given graph. If the given graph is correct, state "True". If the graph is not correct, state "False" and describe the difference.
Hint: To check which side should be shaded, test the point (0, 0) in the inequality to see if it gives a true statement. If the test point tests true, then shade the side that contains the test point. If false, shade the other side of the line. Note: If the line passes through (0, 0), choose a different test point. Any point that does NOT fall on the line will work. |
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| 16) Graph the inequality on paper. If the given graph is correct, state "True". If the graph is not correct, state "False" and describe the difference. |
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| 17) Graph the inequality on paper. If the given graph is correct, state "True". If the graph is not correct, state "False" and describe the difference. |
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| 18) Graph the inequality on paper. If the given graph is correct, state "True". If the graph is not correct, state "False" and describe the difference. |
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| 19) Describe the difference in the graphical solutions of each of the following linear inequalities: |
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22) Solve the absolute-value inequality for x.
Hint: There are two solutions to this inequality.
Click here to review the unit content explanation for Inequalities and Absolute Value Equations. |
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23) Simplify.
Hint: When a fraction is raised to a negative power, the quick way to find the reciprocal of the fraction is to flip it and make the power a positive number.
Click here to review the unit content explanation for Operations with Numbers and Exponents. |
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| 24) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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