Solving Systems of Equations

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What is a system of equations?

Back

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?

Back

Finding the values of the variables that make all equations true.

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What is a solution to a system of equations?

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A pair of values (x, y) that satisfies all equations in the system.

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What does the graph of a system of equations represent?

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The points where the lines intersect represent the solutions.

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What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression from another equation.

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What is the elimination method?

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

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What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the lines are the same.

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How do you check if your solution to a system of equations is correct?

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Plug the values of x and y back into the original equations to see if they hold true.

Front

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

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Identify the equations and the variables involved.