Systems of Equations

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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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

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What is a solution to a system of equations?

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A set of values for the variables that makes all equations true.

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What is meant by 'no solution' in a system of equations?

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There are no values for the variables that satisfy all equations simultaneously.

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What does 'infinitely many solutions' mean?

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There are endless sets of values that satisfy all equations in the system.

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How can you determine if a system has one solution, no solution, or infinitely many solutions?

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By graphing the equations and observing their intersection points.

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What is the graphical representation of a system of equations?

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The lines or curves representing each equation plotted on a coordinate plane.

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What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the lines are the same.

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What is the substitution method in solving systems of equations?

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