Systems of Equations - Identifying solutions

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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 if a system of equations has one solution?

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The equations intersect at exactly one point, representing a unique solution.

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

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The equations are parallel and do not intersect, meaning there are no points that satisfy both equations.

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

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The equations represent the same line, meaning every point on the line is a solution.

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How can you determine if a system of equations has no solution?

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If the slopes of the lines are the same but the y-intercepts are different, the lines are parallel.

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How can you determine if a system of equations has infinitely many solutions?

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If the equations are equivalent, meaning they represent the same line.

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What is an ordered pair?

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A pair of numbers (x,y) that represent a point on a coordinate plane.

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How do you solve a system of equations graphically?

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By plotting the equations on a graph and identifying the point(s) of intersection.

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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, making it easier to solve for the other.