3.2 Graphing Systems of Equations

Last updated about 1 year ago

39 questions

Note from the author:

Instructions

Intro- Warm-Up

Learn it 1:

Practice It (on your own):For each problem, find the solution to the system of equations in (x,y) form.

Application Problems: Level 1 Desmos #2

Application Problems: Level 2

3.2 Graphing Systems of Equations

Last updated about 1 year ago

39 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Graph systems of linear equations in slope-intercept form
Identify solutions to systems of linear equations graphically
Determine whether a system of linear equations has one solution, no solutions, or infinite solutions
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP1
CCSS.PRACTICE.MP4
CCSS.HSF.IF.B.4
CCSS.HSF.IF.C.7.A
CCSS.HSF.BF.A.1
Personal Finance Objectives
Compare different savings rates over time and how they impact the achievement of savings goals.
National Standards for Personal Financial Education
Saving
2a: Select a preferred location for a savings account based on comparison of interest rates and fees at different types of financial institutions.
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems
Application Card Sort

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Graph systems of linear equations in slope-intercept form
Identify solutions to systems of linear equations graphically
Determine whether a system of linear equations has one solution, no solutions, or infinite solutions
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP1
CCSS.PRACTICE.MP4
CCSS.HSF.IF.B.4
CCSS.HSF.IF.C.7.A
CCSS.HSF.BF.A.1
Personal Finance Objectives
Compare different savings rates over time and how they impact the achievement of savings goals.
National Standards for Personal Financial Education
Saving
2a: Select a preferred location for a savings account based on comparison of interest rates and fees at different types of financial institutions.
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems
Application Card Sort

Intro- Warm-Up

DESMOS: Systems of Two Linear Equations
Linked in Google Classroom, after completing answer the following question.
What did you learn from this activity?

Learn it 1:

Systems of Equations
In the last activity, you began exploring how to find a solution that works for two different linear functions. This is called a system of equations.
A system of equations is when two or more equations share the same variables. A solution to that system has to be true for all the equations, not just one.

Think back to the last activity when we graphed two lines on the same coordinate plane. The green line represents the number pairs that had a difference of 8. The purple line represents the number pairs with a sum of 1.

Where did you see the solution to the system of equations on the graph?_______ 

Practice It (on your own):For each problem, find the solution to the system of equations in (x,y) form.

Solution: _______ 

Solution: _______ 

Solution: _______ 

Screen Shot Desmos in Show Your Work
_______ Solution: 

Screen Shot Desmos in Show Your Work
_______ 

Screen Shot Desmos in Show your work
_______ 

Rowan opens a savings account with $25 and saves $75 per month. Reem opens a savings account with $225 and saves $25 per month.  Graph in Desmos and Screen shot your answer. 
Write an equation for Rowan’s savings account balance._______ 
Write an equation for Reem’s savings account balance._______ 
When will their account balances be the same? Week _______ How much will they have?  $_______ 

Number of Solutions: _______ 
Points that are Solutions: _______ 

Number of Solutions: _______ 
Points(s) that are solutions: _______ 

Number of Solutions: _______ 
Points that are solutions: _______ 

How could you identify that a system has no solutions, based on the equations in that system?

How could you identify if a system has infinite solutions algebraically?

Could there be a system of linear equations with exactly two solutions? Why or why not?

Given the graph of y=3x-9 and y=-1/2x+12
Identify the number of solutions_______ 
If possible, find one solution to the system. If there are no solutions, justify how you know. _______ 

Solutions: _______ 
How do you know?_______ 

Solutions: _______ 
How do you know? _______ 

Application Problems: Level 1 Desmos #2

Application Problems: Level 2

Part I: Writing Equations
John and Brenda both recently graduated from Hightower University and started jobs as civil engineers at BuildIt Construction company. 

Calculate how much John saves each month._______ 

Write an equation that represents John’s savings account balance, y, after x months.

Part II: Graphing
Complete the first two equations in the Desmos interactive using your equations from part 1. Do not close this page, you will continue using the graph to answer the following questions.

Both Brenda and John have worked at BuildIt for one year. Answer the following questions by either using the Desmos graph or your equations from Questions 3 and 5.
a.  How much money does John have in his savings account after one year?_______ 
b.  How much more money does John have saved than Brenda after one year?_______ 
c.  One way to measure the wage gap is to consider how many additional months one person has to work to have the same total earnings, or in this case savings, as another. During which month will Brenda surpass John’s 1-year savings total?_______ 

Fill in the table below from the information provided on the Left.

Part II: Building an Emergency Fund
Using the Family Budget Calculator, search for your county or closest major city. For each family, input the number of adults and children to find out the monthly income they would need in order to attain a modest yet adequate standard of living. Then, complete the first row of the table in question #15.  

Bonus Points: A common rule of thumb is to save up an emergency fund that could cover 3 months of living expenses. Complete the second row to show how much each family would need to save.

3.2 Graphing Systems of Equations

3.2 Graphing Systems of Equations

DESMOS: Systems of Two Linear Equations
Linked in Google Classroom, after completing answer the following question.
What did you learn from this activity?

How could you identify that a system has no solutions, based on the equations in that system?

How could you identify if a system has infinite solutions algebraically?

Could there be a system of linear equations with exactly two solutions? Why or why not?

Write an equation that represents John’s savings account balance, y, after x months.

Fill in the table below from the information provided on the Left.

Bonus Points: A common rule of thumb is to save up an emergency fund that could cover 3 months of living expenses. Complete the second row to show how much each family would need to save.

Bonus Points: How many weeks would each family need to save in order to build an emergency fund that covered 3 months of living expenses?

DESMOS: Systems of Two Linear Equations
Linked in Google Classroom, after completing answer the following question.
What did you learn from this activity?

How can you test if that point is a solution to both equations in the system?

Graph both equations in Desmos and Screen Shot in Show your Work below.

How could you identify that a system has no solutions, based on the equations in that system?

How could you identify if a system has infinite solutions algebraically?

Could there be a system of linear equations with exactly two solutions? Why or why not?

Write an equation that represents John’s savings account balance, y, after x months.

Write an equation that represents Brenda’s savings account balance, y, after x months.

Fill in the table below from the information provided on the Left.

Read the graph below and note each initial balance on the graph.

Is there a point where all three families have the same amount in savings? Why or why not?

Bonus Points: A common rule of thumb is to save up an emergency fund that could cover 3 months of living expenses. Complete the second row to show how much each family would need to save.

Bonus Points: How many weeks would each family need to save in order to build an emergency fund that covered 3 months of living expenses?

Bonus Points: Which family would take the longest to build up that emergency fund? How might they adjust their approach to savings?

How can you test if that point is a solution to both equations in the system?

Graph both equations in Desmos and Screen Shot in Show your Work below.

Write an equation that represents Brenda’s savings account balance, y, after x months.

Is there a point where all three families have the same amount in savings? Why or why not?

Bonus Points: Which family would take the longest to build up that emergency fund? How might they adjust their approach to savings?

3.2 Graphing Systems of Equations

3.2 Graphing Systems of Equations

DESMOS: Systems of Two Linear EquationsLinked in Google Classroom, after completing answer the following question. What did you learn from this activity?

How could you identify that a system has no solutions, based on the equations in that system?

How could you identify if a system has infinite solutions algebraically?

Could there be a system of linear equations with exactly two solutions? Why or why not?

Write an equation that represents John’s savings account balance, y, after x months.

Fill in the table below from the information provided on the Left.

Bonus Points: A common rule of thumb is to save up an emergency fund that could cover 3 months of living expenses. Complete the second row to show how much each family would need to save.

Bonus Points: How many weeks would each family need to save in order to build an emergency fund that covered 3 months of living expenses?

DESMOS: Systems of Two Linear EquationsLinked in Google Classroom, after completing answer the following question. What did you learn from this activity?

How can you test if that point is a solution to both equations in the system?

Graph both equations in Desmos and Screen Shot in Show your Work below.

How could you identify that a system has no solutions, based on the equations in that system?

How could you identify if a system has infinite solutions algebraically?

Could there be a system of linear equations with exactly two solutions? Why or why not?

Write an equation that represents John’s savings account balance, y, after x months.

Write an equation that represents Brenda’s savings account balance, y, after x months.

Fill in the table below from the information provided on the Left.

Read the graph below and note each initial balance on the graph.

Is there a point where all three families have the same amount in savings? Why or why not?

Bonus Points: A common rule of thumb is to save up an emergency fund that could cover 3 months of living expenses. Complete the second row to show how much each family would need to save.

Bonus Points: How many weeks would each family need to save in order to build an emergency fund that covered 3 months of living expenses?

Bonus Points: Which family would take the longest to build up that emergency fund? How might they adjust their approach to savings?

How can you test if that point is a solution to both equations in the system?

Graph both equations in Desmos and Screen Shot in Show your Work below.

Write an equation that represents Brenda’s savings account balance, y, after x months.

Is there a point where all three families have the same amount in savings? Why or why not?

Bonus Points: Which family would take the longest to build up that emergency fund? How might they adjust their approach to savings?

DESMOS: Systems of Two Linear Equations
Linked in Google Classroom, after completing answer the following question.
What did you learn from this activity?

DESMOS: Systems of Two Linear Equations
Linked in Google Classroom, after completing answer the following question.
What did you learn from this activity?