5.5 Solving Systems of Equations by Graphing

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What is a system of equations?

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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?

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A system has one solution when 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?

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A system has no solution when 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?

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A system has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

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

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To convert to slope-intercept form (y = mx + b), solve for y in terms of x.

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The slope is 2.

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The y-intercept is 4.

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How can 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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How can you determine if two lines are perpendicular?

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Two lines are perpendicular if the product of their slopes is -1.