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Algebra 1 6-2 Complete Lesson: Solving Systems Using Substitution

By Matt Richardson
Last updated almost 3 years ago
28 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! A board game allows players to trade game pieces of equal value. The diagram shows two fair trades. The hotel is worth $2400. How much is a car worth? Use a dollar sign in your response and enter only the amount.

Problem 1 Got It?

Problem 2 Got It? What is the solution of the system? Use substitution. Show your work.

Problem 2 Got It? Reasoning: In your first step in the previous item, which variable did you solve for? Which equation did you use to solve for the variable?

Problem 3 Got It?

Problem 4 Got It?

Please follow the directions to solve each system using substitution before checking your work by graphing using the embedded Desmos graphing calculator below.

Analysis: For the given system, tell which equation you would first use to solve for a variable in the first step of the substitution method. Explain your choice.

Analysis: For the given system, tell which equation you would first use to solve for a variable in the first step of the substitution method. Explain your choice.

True or False: Tell whether the statement is true or false. Explain.

When solving a system using substitution, if you obtain an identity, then the system has no solution.

True or False: Tell whether the statement is true or false. Explain.

You cannot use substitution to solve a system that does not have a variable with a coefficient of 1 or -1.

Review Lesson 6-1: Solve each system by graphing. You may use the embedded Desmos graphing ulitity above. Identify the solution(s) and number of solutions of each system. Some labels may not be used.

  • exactly one solution
  • infinitely many solutions
  • no solutions
  • Solution: (-3, -6)
  • Solution: (4, -6)
  • Solution: (3, 4)
  • System A
  • System B
  • System C

Review Lesson 5-6: Find the slope of a line perpendicular to the graph of each equation.

  • slope of a perpendicular line: -3
  • slope of a perpendicular line: 4
  • slope of a perpendicular line: 1/4
  • slope of a perpendicular line: -1/3
  • slope of a perpendicular line: 3
  • y = 3x
  • y = -(1/4)x
  • (1/3)x - y = 2

Review Lesson 2-4: Solve the equation. Check your answer. Enter only a number for your response.

Review Lesson 2-4: Solve the equation. Check your answer. Enter only a number for your response.

Review Lesson 2-4: Solve the equation. Check your answer. Enter only a number for your response.

Vocabulary Review: Classify each expression based on whether or not it contains a variable.

  • y + 9
  • a - b
  • 23 + 9
  • 5/x + 14
  • π + 15
  • Contains a variable
  • Does not contain a variable

Vocabulary Review: Classify each equation based on whether or not the variable is isolated.

  • 8k = 16
  • m + 3 = -2
  • a = 7 - 3
  • 12 = z + 4
  • 23 = p
  • The variable is isolated
  • The variable is not isolated

Use Your Vocabulary: Complete the statement with the appropriate form of the word substitution.

ADJECTIVE: "We had a __?__ teacher in social studies today."

Enter a one-word response.

Use Your Vocabulary: Complete the statement with the appropriate form of the word substitution.

NOUN: "The coach made a __?__ of one player for another."

Enter a one-word response.

Use Your Vocabulary: Complete the statement with the appropriate form of the word substitution.

VERB: "The coach made a __?__ of one player for another."

Enter a one-word response.

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