Systems of Linear Equation

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What is a system of linear equations?

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A set of two or more linear equations with the same variables.

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What does it mean to solve a system of linear equations?

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

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What are the three methods to solve systems of linear equations?

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1. Graphing 2. Substitution 3. Elimination

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What is the elimination method?

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A method to solve systems of equations by adding or subtracting equations to eliminate a variable.

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What is the substitution method?

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A method to solve systems of equations by solving one equation for one variable and substituting that value into the other equation.

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What does the solution of a system of equations represent?

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The point(s) where the graphs of the equations intersect, representing the values of the variables.

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What is an inconsistent system of equations?

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A system that has no solution, meaning the lines are parallel.

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What is a dependent system of equations?

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A system that has infinitely many solutions, meaning the equations represent the same line.

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What is an independent system of equations?

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A system that has exactly one solution, meaning the lines intersect at one point.

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How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify if both equations are satisfied.