Solving systems of equations by substitution

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What is a system of equations?

Back

A set of two or more equations with the same variables.

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

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What is the significance of the statement '2 = 2' in solving systems of equations?

Back

It indicates that the equations are equivalent, leading to infinite solutions.

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

Back

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

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.

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

Back

If the equations represent lines that intersect at exactly one point.

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What is the graphical representation of a system of equations?

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The solution can be found at the point(s) where the graphs of the equations intersect.

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What is the first step in using the substitution method?

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Solve one of the equations for one variable in terms of the other variable.

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What does it mean if two equations are dependent?

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They represent the same line and have infinite solutions.

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What does it mean if two equations are independent?

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They represent different lines and can have one solution or no solution.