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# Algebra Lesson 16: Solving Systems Flashcards

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@LoyalLanthanum

### What is the Elimination Method?

• When you add or subtract two equations to eliminate one of the variables (correct)
• Graphing the system of equations and finding the intersection point
• Two lines that intersect at one point
• Replacing one variable with an equivalent expression containing the other variable
• ### What is the Substitution Method?

Replacing one variable with an equivalent expression containing the other variable

### What does the Graphing Method involve?

Graphing the system of equations and finding the point at which they intersect

### What defines a Unique Solution in a system of equations?

<p>Two lines that intersect at one point; the two lines have different slopes</p> Signup and view all the answers

### What does Infinitely Many Solutions mean?

<p>The lines are the same; the two lines have the same slopes and same initial values</p> Signup and view all the answers

### What results in No Solution for a system of equations?

<p>Two lines that are parallel and never intersect; the two lines have the same slope and different initial values</p> Signup and view all the answers

## Study Notes

### Solving Systems of Equations

• Elimination Method: Involves adding or subtracting two equations to remove one variable, simplifying the problem to solve for the remaining variable.

• Substitution Method: Involves expressing one variable in terms of the other variable and substituting this back into the original equation to solve for the variables.

• Graphing Method: A visual approach that involves plotting the equations on a coordinate plane and identifying the point of intersection which represents the solution.

### Types of Solutions

• Unique Solution: Occurs when two lines intersect at a single point; this results in one solution for the system. The lines must have different slopes.

• Infinitely Many Solutions: Happens when two lines are completely overlapping; this indicates that the lines have identical slopes and y-intercepts, leading to an infinite number of solutions.

• No Solution: Characterized by two parallel lines that never intersect; these lines have the same slope but different y-intercepts, indicating that there is no point at which the equations are satisfied simultaneously.

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## Description

Test your knowledge on solving systems of equations with these flashcards. Each card covers key methods such as the elimination method, substitution method, and graphing method. Perfect for students learning algebra and aiming to master these concepts.

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