Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the lines intersect on a graph.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is an ordered pair in the context of systems of equations?

Back

An ordered pair (x, y) represents a solution to the system, where x is the value of the first variable and y is the value of the second.

Front

What does it mean for two equations to be dependent?

Back

Dependent equations are those that represent the same line, leading to infinite solutions.

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What does it mean for two equations to be independent?

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Independent equations are those that represent different lines, leading to either one solution or no solution.