Solving Systems (All Methods)

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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 to solve a system of equations?

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

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What is the substitution method?

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A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method?

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A method for solving a system of equations by adding or subtracting equations to eliminate one variable.

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What is graphing in the context of solving systems of equations?

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A method of solving a system by plotting the equations on a graph and identifying the point(s) where they intersect.

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

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

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How do you check the solution of a system of equations?

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

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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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What is the first step in the elimination method?

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Align the equations and manipulate them (by multiplying or adding) to eliminate one variable.