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 eliminate a variable in a system of equations?

Back

To remove one variable by combining equations, making it easier to solve for the remaining variable.

Front

What is the substitution method?

Back

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

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What is the elimination method?

Back

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

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What is the graphical method of solving systems of equations?

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A method where each equation is graphed on the same coordinate plane, and the solution is the point(s) where the graphs intersect.

Front

How do you find the least common multiple (LCM) of coefficients?

Back

The LCM of coefficients is the smallest multiple that is evenly divisible by each of the coefficients.

Front

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.

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What does it mean if two equations represent parallel lines?

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The system has no solution because the lines never intersect.

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What does it mean if two equations represent the same line?

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The system has infinitely many solutions because every point on the line is a solution.

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What is the solution to a system of equations?

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