Algebra 1 6-1 Independent Practice: Solving Systems by Graphing

Last updated about 4 years ago

17 questions

20

A.REI.6

10

A.REI.6

20

10

A.REI.6

20

A.REI.6

10

A.REI.6

20

A.REI.6

10

A.REI.6

40

A.REI.6

10

A.REI.6

5

10

A.REI.6

Library

Algebra 1 6-1 Independent Practice: Solving Systems by Graphing

Last updated about 4 years ago

17 questions

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.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.REI.6

10

A.REI.6

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

A.REI.6

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.REI.6

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

A.REI.6

20

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

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

A.REI.6

10

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

A.REI.6

40

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.

You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.REI.6

10

Analysis: What does the intersection point of the system of equations you graphed in the previous item represent?

A.REI.6

5

10

Reflection: Math Success

A.REI.6

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.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.

(6, 13)

(-3, 7)

(2, 5)

(0, 7)

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

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

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

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.

You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Analysis: What does the intersection point of the system of equations you graphed in the previous item represent?

Vocabulary: How many solutions does an inconsistent system have?

no solutions

infinitely many

exactly one

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

exactly one

no solutions

infinitely many

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

no solutions

infinitely many

exactly one

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. You may use the canvas to help illustrate your chosen response.

No; A point must be on both lines to be a solution of the system.

Yes; As long as the point is on at least one line, it is a solution of the system.

Reasoning: Can a system of two linear equations have exactly two solutions? Explain.
You may use the canvas to help illustrate your chosen response.

No; Two lines can not intesect in exactly two places. They must intersect in 0, 1, or infinitely-many places (aka overlap one another). This means that a system of linear equations must have 0, 1, or infinitely-many solutions.

Yes; Two lines may intersect at exactly two places. This means that a system of equations may have exactly 2 solutions.

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. You may use the canvas to help illustrate your chosen response.

You can conclude that the graphs of the linear equations will share the common point (-2, 3).

You can conclude that the graphs of the linear equations will have at least 2 points of intersection.

You can conclude that one of the graphs is a horizontal line and that the other is a vertical line.

Reflection: Math Success

Identify the solution to the system of equations you solved by graphing in the previous item.

(6, 13)

(-3, 7)

(2, 5)

(0, 7)

Vocabulary: How many solutions does an inconsistent system have?

no solutions

infinitely many

exactly one

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

exactly one

no solutions

infinitely many

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

no solutions

infinitely many

exactly one

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. You may use the canvas to help illustrate your chosen response.

No; A point must be on both lines to be a solution of the system.

Yes; As long as the point is on at least one line, it is a solution of the system.

Reasoning: Can a system of two linear equations have exactly two solutions? Explain. 
You may use the canvas to help illustrate your chosen response.

No; Two lines can not intesect in exactly two places. They must intersect in 0, 1, or infinitely-many places (aka overlap one another). This means that a system of linear equations must have 0, 1, or infinitely-many solutions.

Yes; Two lines may intersect at exactly two places. This means that a system of equations may have exactly 2 solutions.

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. You may use the canvas to help illustrate your chosen response.

You can conclude that the graphs of the linear equations will share the common point (-2, 3).

You can conclude that the graphs of the linear equations will have at least 2 points of intersection.

You can conclude that one of the graphs is a horizontal line and that the other is a vertical line.

Algebra 1 6-1 Independent Practice: Solving Systems by Graphing

Algebra 1 6-1 Independent Practice: Solving Systems by Graphing

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.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

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.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response as an ordered pair.

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.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response as an ordered pair.

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response as an ordered pair.

Analysis: What does the intersection point of the system of equations you graphed in the previous item represent?

Reflection: Math Success

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.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.

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.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response as an ordered pair.

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.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response as an ordered pair.

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.Write your response as an ordered pair.

Analysis: What does the intersection point of the system of equations you graphed in the previous item 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. You may use the canvas to help illustrate your chosen response.

Reasoning: Can a system of two linear equations have exactly two solutions? Explain. You may use the canvas to help illustrate your chosen response.

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. You may use the canvas to help illustrate your chosen response.

Reflection: Math Success

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

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.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Identify the solution to the system of equations you solved by graphing in the previous item.
Write your response as an ordered pair.

Reasoning: Can a system of two linear equations have exactly two solutions? Explain.
You may use the canvas to help illustrate your chosen response.