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Algebra 2 3-5 Complete Lesson: Systems With Three Variables

Last updated over 4 years ago

22 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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.

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100

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Solve It! How much does each box weigh?

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1.

Drag and drop to identify the mass of each box.

1 lb
2 lb
3 lb
4 lb
5 lb
6 lb

A Boxes
B Boxes
C Boxes

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2.

Problem 1 Got It?

A

B

C

D

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3.

Problem 2 Got It? What is the solution of the system? Use elimination.

(1, 4, -2)

(0, 4, -1)

(4, -1, 2)

(-1, 2, -4)

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4.

Problem 2 Got It? Reasoning: Could you have used elimination in another way? Explain. HINT: Could you have eliminated a difference variable first?

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Problem 3 Got It? What is the solution of the system? Use substitution.

-4
-2
0
1
2
4

x =
y =
z =

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6.

Problem 4 Got It?

A

B

C

D

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B

C

D

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B

C

D

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B

C

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10.

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B

C

D

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11.

Reasoning: How do you decide whether substitution is the best method to solve a system in three variables?

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12.

Error Analysis: A classmate says that the system consisting of x = 0, y = 0, and z = 0 has no solution. Explain the student's error.

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13.

Writing: How many solutions does this system have? Hint: Is the system dependent? inconsistent?
Explain your answer in terms of intersecting planes.

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14.

Visualize: The graph of a system is shown here. How many solutions does this system have? Explain.

Infinitely many, each point that lies within any one plane is a slolution.

None, a point must lie within all three planes to be a solution.

Infinitely many, each point that lies within any two planes is a slolution.

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15.

Review Lesson 3-4:
1. Graph the system of inequalities to form a feasible region.
2. Zoom and pan your graph to establish an appropriate viewing window.
3. Click on each vertex of the feasible region to make its label appear.
4. Re-zoom and re-pan again, if necessary, to ensure that the feasible region and vertex labels are showing.

Yɛayi Graphing asɛmmisa type foforo a wɔatu mpɔn adi! Asuafo rentumi mmua saa asɛmmisa yi bio.

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16.

Review Lesson 3-4: Refer to the constraints and feasible region in the previous item. At what vertex does the maximum value occur for the objective function, P, below?

(0, 4)

(2, 3)

(5, 0)

(0, 0)

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Review Lesson 1-5: Solve the inequality. Graph the solution on a number line.

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Review Lesson 3-2: Solve the system using elimination. Show your work on the canvas and write the solution in the space provided.

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19.

Vocabulary Review: How many points determine a plane?

1

2

3

4

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20.

Use Your Vocabulary: Classify each ordered triple based on its x-coordinate.

(1, 0, 1)
(1, 1, 0)
(0, 1, 1)
(1, 0, 0)

Has x-coordinate 0
Has x-coordinate 1

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21.

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.

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22.

Reflection: Math Success