Algebra 1 6-1 Complete Lesson: Solving Systems by Graphing

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Solve It! Two professional downhill skiers are racing at the speeds shown in the diagram. Skier 1 starts 5 s before Skier 2. The course is 5000 ft long. Will Skier 2 pass Skier 1?

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Solve It! How do you know?

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Problem 1 Got It?

10

Problem 2 Got It?

10

Problem 3 Got It? Identify the solution(s) of the system by graphing.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

10

Problem 3 Got It? Identify the solution(s) of the system by graphing.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

10

Problem 3 Got It? Reasoning: Before graphing the equations, how can you determine whether a system of equations has exactly one solution, infinitely many solutions, or no solution?

Complete all of the graphing in this assignment by hand before checking your work using the embedded Desmos graphing calculator below. After checking your work, you may edit your own graphs.

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Solve the system by graphing.
Work carefully and precisely to ensure that you graphs reveal the correct solution.
As always, check your solution using substitution.

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

20

Solve the system by graphing.
Work carefully and precisely to ensure that you graphs reveal the correct solution.
As always, check your solution using substitution.

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

20

Solve the system by graphing.
Work carefully and precisely to ensure that you graphs reveal the correct solution.
As always, check your solution using substitution.

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

20

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

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Concert Tickets: Tickets for a concert cost $10 each if you order them online, but you must pay a service charge of $8 per order. The tickets are $12 each if you buy them at the door on the night of the concert, with no service charge.

a. Write a system of equations to model the situation. Let c be the total cost. Let t be the number of tickets.

b. Graph the equations and find the intersection point.

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Analysis: What does the intersection point of the system of equations you graphed in number 9 represent?

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Vocabulary: How many solutions does an inconsistent system have?

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Vocabulary: How many solutions does a consistent and dependent system have?

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Vocabulary: How many solutions does an consistent and independent system have?

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Writing: Suppose you graph a system of linear equations. If a point is on only one of the lines, is it a solution of the system? Explain.

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Reasoning: Can a system of two linear equations have exactly two solutions? Explain.

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Reasoning: Suppose you find that two linear equations are true when x = -2 and y = 3. What can you conclude about the graphs of the equations? Explain.

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Review Lesson 5-8: Graph the functions by translating the graph of y = |x|. Graph with colors that match the functions.

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Review Lesson 5-6: Find the slope of a line that is parallel to the graph of the equation.

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Review Lesson 5-6: Find the slope of a line that is parallel to the graph of the equation.

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Review Lesson 5-6: Find the slope of a line that is parallel to the graph of the equation.

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Review Lesson 2-5: Solve the equation for y.

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Review Lesson 2-5: Solve the equation for y.

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Vocabulary Review: Label each amount described as infinite or finite.

infinite
finite

the rational numbers greater than 6
the number of seats in a movie theater
the number of grams in one kilogram
the set of odd numbers

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Use Your Vocabulary: Complete each sentence with the appropriate word from the list.

systematic
system
systematize

The librarian planned to __?__ the donated magazines.
The American __?__ of government is based on the Constitution.
Sam was __?__ in his approach to studying for his final exam.
A __?__ of linear equations might consist of two equations.

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Vocabulary: Use the embedded Desmos graphing utility above to graph and take screenshots of three systems of linear equations. One must have no solutions, one must have exactly 1 solution, and one must have infinitely many solutions. Add your screenshots to the respective area of the canvas.

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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

10

Solve It! Two professional downhill skiers are racing at the speeds shown in the diagram. Skier 1 starts 5 s before Skier 2. The course is 5000 ft long. Will Skier 2 pass Skier 1?

Solve It! How do you know?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It? Identify the solution(s) of the system by graphing. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It? Identify the solution(s) of the system by graphing. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It? Reasoning: Before graphing the equations, how can you determine whether a system of equations has exactly one solution, infinitely many solutions, or no solution?

Solve the system by graphing.Work carefully and precisely to ensure that you graphs reveal the correct solution.As always, check your solution using substitution.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response in the following format, with a space immediately following the comma: (5, -4)

Solve the system by graphing.Work carefully and precisely to ensure that you graphs reveal the correct solution.As always, check your solution using substitution.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response in the following format, with a space immediately following the comma: (5, -4)

Solve the system by graphing.Work carefully and precisely to ensure that you graphs reveal the correct solution.As always, check your solution using substitution.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response in the following format, with a space immediately following the comma: (5, -4)

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response in the following format, with a space immediately following the comma: (5, -4)

Analysis: What does the intersection point of the system of equations you graphed in number 9 represent?

Vocabulary: How many solutions does an inconsistent system have?

Vocabulary: How many solutions does a consistent and dependent system have?

Vocabulary: How many solutions does an consistent and independent system have?

Writing: Suppose you graph a system of linear equations. If a point is on only one of the lines, is it a solution of the system? Explain.

Reasoning: Can a system of two linear equations have exactly two solutions? Explain.

Reasoning: Suppose you find that two linear equations are true when x = -2 and y = 3. What can you conclude about the graphs of the equations? Explain.

Review Lesson 5-8: Graph the functions by translating the graph of y = |x|. Graph with colors that match the functions.

Review Lesson 5-6: Find the slope of a line that is parallel to the graph of the equation.

Review Lesson 5-6: Find the slope of a line that is parallel to the graph of the equation.

Review Lesson 5-6: Find the slope of a line that is parallel to the graph of the equation.

Review Lesson 2-5: Solve the equation for y.

Review Lesson 2-5: Solve the equation for y.

Vocabulary Review: Label each amount described as infinite or finite.

Use Your Vocabulary: Complete each sentence with the appropriate word from the list.

Vocabulary: Use the embedded Desmos graphing utility above to graph and take screenshots of three systems of linear equations. One must have no solutions, one must have exactly 1 solution, and one must have infinitely many solutions. Add your screenshots to the respective area of the canvas.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 3 Got It? Identify the solution(s) of the system by graphing.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It? Identify the solution(s) of the system by graphing.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Solve the system by graphing.
Work carefully and precisely to ensure that you graphs reveal the correct solution.
As always, check your solution using substitution.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

Solve the system by graphing.
Work carefully and precisely to ensure that you graphs reveal the correct solution.
As always, check your solution using substitution.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

Solve the system by graphing.
Work carefully and precisely to ensure that you graphs reveal the correct solution.
As always, check your solution using substitution.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response in the following format, with a space immediately following the comma: (5, -4)

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.