Solving Systems of Linear Equations, additional practice

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What is a system of linear equations?

Back

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

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What does it mean for two lines to be parallel in a system of linear equations?

Back

Parallel lines have the same slope but different y-intercepts, resulting in no solutions.

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What does it mean for two lines to be identical in a system of linear equations?

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Identical lines are the same line, resulting in infinitely many solutions.

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What does it mean for two lines to intersect in a system of linear equations?

Back

Intersecting lines have one point in common, resulting in a unique solution.

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What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

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What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

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How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they will have infinitely many points of intersection.

Front

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

Back

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

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