Flashcard 6-3: System of linear equations

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What is a system of linear equations?

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A set of two or more linear equations with the same variables.

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What does it mean if two lines are parallel in a system of linear equations?

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It means there is no solution to the system, as the lines never intersect.

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What does it mean if two lines are the same in a system of linear equations?

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It means there are infinitely many solutions, as every point on the line is a solution.

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What does it mean if two lines intersect at one point in a system of linear equations?

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It means there is exactly one solution to the system, which is the point of intersection.

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How do you convert an equation to slope-intercept form?

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The solution is the point where the two lines intersect.

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

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If the lines are parallel, the system has no solution.

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What is the graphical representation of a system of equations with infinitely many solutions?

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The graphical representation is two overlapping lines.