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Algebra 2 Chapter 1.4 Flashcards

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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?

Plug the found variable into either new eq 1 or new eq 2 to find another variable. Signup and view all the answers

What is step four in solving a three-variable system?

Plug the two found variables into one of the original three equations. Signup and view all the answers

What is step five in solving a three-variable system?

Write your answer in (x,y,z) form and include the parentheses. Signup and view all the answers

When solving a three-variable system, if you cancel out all variables and are left with 0 = any number, what does this indicate?

No solution Signup and view all the answers

What does it mean if you get more than one answer for the same variable when solving a three-variable system?

Infinitely many solutions Signup and view all the answers

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.