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 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 substitution method?

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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?

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

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What is a solution to a system of equations?

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A set of values for the variables that makes all equations in the system true.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

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What is the graphical method for solving systems of equations?

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Plotting each equation on a graph and identifying the point(s) where the lines intersect.

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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 equations represent the same line.

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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.