Solving Systems of Equations

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What is a system of equations?

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

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

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An ordered pair (x, y) that satisfies all equations in the system.

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

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Substitute the values of x and y into each equation to see if they hold true.

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What is the graphical representation of a system of equations?

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The graphs of the equations plotted on the same coordinate plane.

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What does it mean if two lines intersect on a graph?

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The system of equations has one unique solution.

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What does it mean if two lines are parallel on a graph?

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The system of equations has no solution.

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What does it mean if two lines coincide on a graph?

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The system of equations has infinitely many solutions.

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How can you solve a system of equations graphically?

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By plotting the equations on a graph and identifying the point(s) of intersection.

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What is substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and then substituted into the other equation.

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What is elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable.