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 that are solved together.

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What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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

Back

It means there are no values for the variables that can satisfy all equations in the system, often represented by parallel lines.

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

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It means there are countless sets of values for the variables that satisfy all equations, often represented by coinciding lines.

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How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

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What is the graphical representation of a system of equations with a unique solution?

Back

Two lines that intersect at exactly one point.

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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.

Front

What is the slope-intercept form of a linear equation?

Back

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How do you find the intersection point of two lines represented by equations?

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Solve the system of equations simultaneously to find the values of the variables at the intersection.