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.

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

Back

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 (coinciding lines).

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

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By analyzing the slopes and y-intercepts of the equations.

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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 never meet, 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.

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How do you solve a system of equations using substitution?

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Solve one equation for one variable and substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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Add or subtract the equations to eliminate one variable, then solve for the remaining variable.