Solving 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 for a system of equations to have a unique solution?

Back

It means the equations intersect at exactly one point on the graph.

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What does it mean for a system of equations to have no solution?

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It means the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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It means the equations represent the same line, so every point on the line is a solution.

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How can 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 substitution in solving systems of equations?

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A method where you solve one equation for one variable and substitute that value into the other equation.

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What is elimination in solving systems of equations?

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A method where you add or subtract equations to eliminate one variable, making it easier to solve.

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What is the graphical representation of intersecting lines?

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Two lines that cross at a single point, indicating a unique solution.

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What is the graphical representation of parallel lines?

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Two lines that run alongside each other without ever meeting, indicating no solution.

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What is the graphical representation of coinciding lines?

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Two lines that lie on top of each other, indicating infinitely many solutions.