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 that are solved together.

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What does it mean to graph a system of equations?

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It involves plotting the equations on the same coordinate plane to find their intersection points, which represent the solutions.

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What is the elimination method in solving systems of equations?

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A technique where one equation is manipulated to eliminate one variable, allowing for the other variable to be solved.

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What is the substitution method in solving systems of equations?

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

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What does it mean if two lines intersect at one point?

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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?

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The system of equations has no solution.

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What does it mean if two lines overlap?

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The system of equations has infinitely many solutions.

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How do you determine the solution of a system of equations graphically?

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By finding the point(s) where the graphs of the equations intersect.

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What is the first step in solving a system of equations using elimination?

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Align the equations so that corresponding variables and constants are in the same columns.

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What is the first step in solving a system of equations using substitution?

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Solve one of the equations for one variable in terms of the other variable.