Systems of equations review

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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 are the three main methods to solve systems of equations?

Back

1. Substitution 2. Elimination 3. Graphing

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

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What is the substitution method?

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?

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

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How can you determine if a system of equations is consistent or inconsistent?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

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What is a graphical representation of a system of equations?

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It is a visual representation where each equation is graphed, and the solution is where the lines intersect.

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What is the meaning of a solution in the context of a system of equations?

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A solution is an ordered pair (x, y) that satisfies all equations in the system.

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What is a system of inequalities?

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A set of two or more inequalities that are solved together, often represented graphically.