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.

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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 graphical representation of a system of equations?

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The intersection points of the graphs of the equations.

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What is a unique solution in a system of equations?

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A single point where the graphs of the equations intersect.

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

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The graphs of 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, so every point on the line is a solution.

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How do you solve a system of equations using substitution?

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Solve one equation for one variable and substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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Add or subtract the equations to eliminate one variable, then solve for the other.

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What is the substitution method?

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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.