Systems of Equations Basics Review

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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 to solve a system of equations graphically?

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To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they intersect.

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What is an ordered pair?

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An ordered pair is a pair of numbers used to represent a point in a coordinate system, written as (x, y).

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What does it mean if a system of equations has no solution?

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A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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How do you determine if an ordered pair is a solution to a system of equations?

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To determine if an ordered pair is a solution, substitute the x and y values into each equation. If both equations are true, the pair is a solution.

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The solution is (1, 3).

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations consists of the lines or curves plotted on a coordinate plane that correspond to each equation.

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

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What does it mean for two equations to be inconsistent?

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Two equations are inconsistent if they have no solutions, meaning their graphs do not intersect.