Algebra 2 3-1 Complete Lesson: Solving Systems Using Tables and Graphs

Last updated almost 4 years ago

24 questions

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! There are 25 bikes and trikes at the park. The bikes and trikes have 60 wheels in all. In the graph, the red dots show sums of 25. The blue dots show 60-wheel combinations.

How many bikes and trikes are in the park?

Bikes
Trikes

Problem 1 Got It? You may use the embedded Desmos graphing calculator above.

Problem 2 Got It? If the growth rates continue, how long will each shark be when it is 25 years old?
HINT: Use the related equations and substitution or graphing. You may use either of the Desmos calculators embedded below.

47.95 cm
55.75 cm
59.5 cm
62.25 cm

Greenland shark length
Spiny Dogfish shark length

Problem 2 Got It? Reasoning: Explain why growth rates for these sharks may not continue indefinitely.

Problem 3 Got It? You may use Desmos or the embedded Desmos graphing utility above.

…

Problem 4 Got It? HINT: Consider the slope and y-intercept of each line.

Solve the system by graphing. Include relevant graph detail. Check your solution.

y = x - 1
y = -x + 3

Solve the system by graphing. Include relevant graph detail. Check your solution.

2x + y = 4
x - y = 2

Consider using intercepts to graph or re-writing each equation in slope-intercept form.
You may use the canvas for scratch work.

You bought a total of 6 pens and pencils for $4. If each pen costs $1 and each pencil costs $.50, how many pens and pencils did you buy?

Vocabulary: Is it possible for a system of equations to be both independent and inconsistent? Explain.

Open-Ended: Write a system of linear equations that has no solution.

Reasoning: In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Is this system independent, dependent, or inconsistent?

Review Lesson 2-8: Graph the three inequalities on the same coordinate plane. 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.

Review Lesson 2-3: Identify the slope of the line through each pair of points.

(-2, -4) and (1, 2)
(0, 0) and (5, -3)
(1, 3) and (4, 9)

Review Lesson 1-3: What is the value for a + b - 2c for a = 3, b = 1, and c = -3.

Review Lesson 1-3: Substitute -3 for x in each of the equations. Identify the value of y in each case.

y = -10
y = 8
y = -3
y = -8

Vocabulary Review: Classify each equation based on its form.

y - 2 = 5(x - 3)
x + 5y = -3
y = 2x + 10

slope-intercept form
point-slope form
standard form

Classify each item on the left based on the type of system it describes or represents.

A system of 2 parallel lines
A system of 2 perpendicular lines
A system with exactly 1 solution
A system with infinietly-many solutions
A system with no solutions

Inconsistent
Consistent and dependent
Consistent and independent

Use Your Vocabulary: Recall the infomation about systems of linear equations below.

Tag each statement as true or false.

true
false

Inconsistent linear systems intersect at two points.
An independent linear system has one solution.
A dependent linear system has no solutions.
Two unique lines with the same slope form an inconsistent system.

Graphing systems Review: Which graph represents the system?

100

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.

Algebra 2 3-1 Complete Lesson: Solving Systems Using Tables and Graphs

How many bikes and trikes are in the park?

Problem 1 Got It? You may use the embedded Desmos graphing calculator above.

Problem 2 Got It? If the growth rates continue, how long will each shark be when it is 25 years old? HINT: Use the related equations and substitution or graphing. You may use either of the Desmos calculators embedded below.

Problem 2 Got It? Reasoning: Explain why growth rates for these sharks may not continue indefinitely.

Problem 3 Got It? You may use Desmos or the embedded Desmos graphing utility above.

Problem 4 Got It? HINT: Consider the slope and y-intercept of each line.

Problem 4 Got It? HINT: Consider the slope and y-intercept of each line.

Problem 4 Got It? HINT: Consider the slope and y-intercept of each line.

Solve the system by graphing. Include relevant graph detail. Check your solution. y = x - 1y = -x + 3

Solve the system by graphing. Include relevant graph detail. Check your solution. 2x + y = 4x - y = 2Consider using intercepts to graph or re-writing each equation in slope-intercept form.You may use the canvas for scratch work.

You bought a total of 6 pens and pencils for $4. If each pen costs $1 and each pencil costs $.50, how many pens and pencils did you buy?

Vocabulary: Is it possible for a system of equations to be both independent and inconsistent? Explain.

Open-Ended: Write a system of linear equations that has no solution.

Reasoning: In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Is this system independent, dependent, or inconsistent?

Review Lesson 2-8: Graph the three inequalities on the same coordinate plane. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 2-3: Identify the slope of the line through each pair of points.

Review Lesson 1-3: What is the value for a + b - 2c for a = 3, b = 1, and c = -3.

Review Lesson 1-3: Substitute -3 for x in each of the equations. Identify the value of y in each case.

Vocabulary Review: Classify each equation based on its form.

Classify each item on the left based on the type of system it describes or represents.

Use Your Vocabulary: Recall the infomation about systems of linear equations below.Tag each statement as true or false.

Graphing systems Review: Which graph represents the system?

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 2 Got It? If the growth rates continue, how long will each shark be when it is 25 years old?
HINT: Use the related equations and substitution or graphing. You may use either of the Desmos calculators embedded below.

Solve the system by graphing. Include relevant graph detail. Check your solution.

y = x - 1
y = -x + 3

Solve the system by graphing. Include relevant graph detail. Check your solution.

2x + y = 4
x - y = 2

Consider using intercepts to graph or re-writing each equation in slope-intercept form.
You may use the canvas for scratch work.

Use Your Vocabulary: Recall the infomation about systems of linear equations below.

Tag each statement as true or false.

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.