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 graphing in the context of systems of equations?

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A method of solving systems 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 one solution?

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The lines representing the equations intersect at exactly one point, indicating a unique solution for the variables.

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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, indicating that there are no values for the variables that satisfy both equations.

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What does it mean if a system of equations has infinitely many solutions?

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The lines representing the equations coincide, meaning they are the same line and have an infinite number of points in common.

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How do you determine the best method to solve a system of equations?

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Consider the structure of the equations; if one equation is already solved for a variable, use substitution; if the coefficients are easily manipulated, use elimination.

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What is a consistent system of equations?

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A system that has at least one solution.