Questions and Answers
What is a solution of a linear equation in three variables?
(x,y,z)
What is step one in solving a three-variable system?
Look at the three equations given to you and look for opposite values to cancel out.
What is step two in solving a three-variable system?
Combine the new equations to cancel out a new variable.
What is step three in solving a three-variable system?
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What is step four in solving a three-variable system?
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What is step five in solving a three-variable system?
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When solving a three-variable system, if you cancel out all variables and are left with 0 = any number, what does this indicate?
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What does it mean if you get more than one answer for the same variable when solving a three-variable system?
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Study Notes
Solutions of Linear Equations
- A solution of a linear equation in three variables is represented as (x, y, z).
Steps to Solve a Three-Variable System
- Step One: Examine three given equations for opposite values to cancel out a variable. If automatic cancellation isn't possible, manipulate an equation to create an opposite value. Cancel out a variable twice using different equations to produce new equations.
- Step Two: Combine the new equations to cancel out a variable, allowing resolution of another variable.
- Step Three: Substitute the found variable back into either of the new equations to solve for a second variable.
- Step Four: With two variables determined, substitute them into one of the original three equations to find the final variable.
- Step Five: Present the final answer in the format (x, y, z), ensuring to include parentheses.
Outcomes in Solution Process
- If cancellation leads to an equation formatted as 0 = any number, this indicates there is no solution.
- If multiple answers for the same variable are obtained, it indicates infinitely many solutions exist.
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Description
Test your knowledge on Algebra 2 concepts from Chapter 1.4 with these flashcards. Each card provides a definition and key terms related to solving linear equations in three variables. Perfect for refreshing your memory before exams or enhancing your understanding of the topic.
