Solving Systems of Linear Equations

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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 possible outcomes when solving a system of linear equations?

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1. One solution (intersecting lines), 2. No solution (parallel lines), 3. Infinite solutions (coincident lines).

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What is the elimination method?

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A technique for solving 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 technique for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

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What does it mean if two lines are parallel in a system of equations?

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They have no points in common, meaning there is no solution to the system.

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What does it mean if two lines are coincident?

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They lie on top of each other, meaning there are infinitely many solutions to the system.

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How do you determine if a system of equations has one solution?

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If the lines represented by the equations intersect at exactly one point.

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

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Substitute the solution back into the original equations to see if they hold true.