Test Solve Systems of Equations Using Elimin., Subst., Graph

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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 solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the elimination method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What is the substitution method?

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A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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

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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 infinite solutions?

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The equations represent the same line, meaning every point on the line is a solution.

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How do you graph a system of equations?

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Plot each equation on the same coordinate plane and identify the point(s) where they intersect.

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What is the first step in the elimination method?

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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 the substitution method?

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

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How can you check your solution to a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.