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 if a system of equations has no solution?

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The lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has one solution?

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The lines represented by the equations intersect at exactly one point.

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

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The lines represented by the equations are the same line, overlapping each other.

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Back

The slope of the line.

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Back

The y-intercept, where the line crosses the y-axis.

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How can you determine if two equations represent the same line?

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If one equation can be transformed into the other by algebraic manipulation.

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What is the graphical representation of a system of equations?

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It is represented by the intersection points of the lines on a coordinate plane.

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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 then 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.