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Algebra 1 6-2 Guided Practice: Solving Systems Using Substitution

By Matt Richardson
Last updated over 2 years ago
11 Questions

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. Hint: Consider substituting three cars and $100 for each house.

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Take Note: Review: Summarize the process of solving a system of equations by graphing (from lesson 6-1).

Take Note: Summarize the process of solving a system of equations by using the substitution method.

Problem 1 Got It?

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Take Note: Order the steps for solving systems using the substitution method.

It may be helpful to consider a specific system. Here is the system from Problem 1:
3y+4x-=14
-2x+y=-3

  1. Isolate the variable in the equation you created (the one that has only one variable). This provides the numeric value for the variable.
  2. Finally, check your work by substituting your ordered pair into BOTH equations and ensuring that it checks out.
  3. Substitute the expression that is equivalent to one of the variables for that variable in the other equation. This creates an equation with only one variable.
  4. Solve the equation for the final variable. This provides the numeric value for the final variable. You now have an answer.
  5. Record your answer as an ordered pair: (x, y)
  6. First, isolate one variable in one equation (choose the easiest variable to isolate). This provides an expression that is equivalent to one variable in the system.
  7. Substitute the numeric value of the variable into either of the original equations (choose the equation that is easiest to work with). This creates a second equation that only has one variable, the final variable.

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

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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?

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Problem 3 Got It?

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Take Note: Consider solving systems of linear equations that have no solution and those that have infinitely many solutions. Classify each item in the left column below based on the type of system it represents.

  • The system simplifies to a false statement like 2=7.
  • The graph reveals two lines that are parallel to one another.
  • The graph reveals two lines that are the same (lines that overlap one another).
  • The system simplifies to an identity like 5 = 5.
  • Systems with infinitely many solutions
  • Systems with no solution

Problem 4 Got It?

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Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?