Solving System 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 elimination method?

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A technique for solving systems of equations by eliminating one variable, allowing for the other variable to be solved.

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How do you eliminate a variable in a system of equations?

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By adding or subtracting the equations to cancel out one of the variables.

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What is the first step in using the elimination method?

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Align the equations so that corresponding variables and constants are in the same columns.

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

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The lines represented by the equations are parallel and never intersect.

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

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The equations represent the same line, meaning every point on the line is a solution.

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

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By substituting the values back into the original equations to see if they hold true.

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What is the graphical representation of a system of equations?

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The intersection points of the lines representing the equations on a coordinate plane.