Flashcard - Systems of Equations

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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 two lines to be parallel?

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Two lines are parallel if they have the same slope and will never intersect.

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What does it mean for two lines to be perpendicular?

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

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How do you convert an equation to 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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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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The y-intercept is 3, which is the value of y when x = 0.

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The solution is the ordered pair (x, y) that satisfies both equations.

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What is an ordered pair in the context of systems of equations?

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An ordered pair (x, y) represents a point on the coordinate plane that is a potential solution to a system of equations.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines represented by the equations.

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What is the term for the point where two lines intersect?

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The point of intersection is called the solution to the system of equations.