Algebra Lesson 16: Solving Systems Flashcards

Questions and Answers

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?

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

What does Infinitely Many Solutions mean?

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

What results in No Solution for a system of equations?

Two lines that are parallel and never intersect; the two lines have the same slope and different initial values 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.

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.