System of Equations Review

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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

Back

It means that the graphs of 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 that the graphs of the equations are parallel and never intersect.

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

Back

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

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How can you find the solution to a system of equations graphically?

Back

By finding the point where the graphs of the equations intersect.

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Back

The slope (m) represents the steepness of the line, indicating how much y changes for a change in x.

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The y-intercept (b) is the point where the line crosses the y-axis.

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How do you determine if two lines are parallel?

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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 one solution?

Back

Two lines that intersect at a single point.

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What is the graphical representation of a system of equations with no solution?

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Two parallel lines that never intersect.