Systems of Equations

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What is a system of equations?

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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?

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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 countless sets of values that satisfy all equations in the system.

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

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If the graphs of the equations intersect at exactly one point.

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What is the graphical representation of a system of equations?

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The graphs of the equations plotted on the same 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 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.

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What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable.