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 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 elimination method?

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

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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 an infinite number of 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 do you determine if a system of equations has one solution?

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

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What is the graphical representation of a system of linear equations?

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The solution is the point(s) where the lines intersect on a graph.

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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.

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What is the first step in solving a system of equations using elimination?

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